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Logarithmic and trigonometric tabl 




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LOGARITHMIC AND 
TRIGONOMETRIC TABLES 



A SERIES OF MATHEMATICAL TEXTS 
(FOR COLLEGES) 

EDITED BY 

EARLE RAYMOND HEDRICK 



THE CALCULUS 

By Ellery Williams Davis and William Charles Brenke. 

ANALYTIC GEOMETRY AND ALGEBRA 

By Alexander Ziwet and Louis Allen Hopkins. 

ELEMENTS OF ANALYTIC GEOMETRY 

By Alexander Ziwet and Louis Allen Hopkins. 

PLANE AND SPHERICAL TRIGONOMETRY 
By Alfred Monroe Kenyon and Louis Ingold. 

ELEMENTARY MATHEMATICAL ANALYSIS 

By John Wesley Young and Frank Millett Morgan. 

PLANE TRIGONOMETRY 

By John Wesley Young and Frank Millett Morgan. 

COLLEGE ALGEBRA 

By Ernest Brown Skinner. 

MATHEMATICS FOR AGRICULTURE AND GENERAL 
SCIENCE 
By Alfred Monroe Kenyon and William Vernon Lovttt. 

MATHEMATICS FOR STUDENTS OF AGRICULTURE 

By Samuel Eugene Rasor. 

THE MACMILLAN TABLES 

Prepared under the direction of Earle Raymond Hedrick. 

A BRIEF COURSE IN COLLEGE ALGEBRA 
By Walter Burton Ford. 

COLLEGE ALGEBRA 

By Arthur M. Harding and George W. Mulltns. 

PLANE TRIGONOMETRY 

By Arthur M. Harding and George W. Mullins. 

GENERAL MATHEMATICS 

By Clinton H. Currier and Emery E. Watson. 

PROJECTIVE PURE GEOMETRY 
By Thomas F. Holgate 

ANALYTIC GEOMETRY 

By Arthur M. Harding and George W. Mulltns. 

INTRODUCTION TO HIGHER GEOMETRY 
By William C. Graustein. 

INTRODUCTION TO TRIGONOMETRY AND ANALYTIC 
GEOMETRY 
By Ernest Brown Skinner. 

DIFFERENTIAL AND INTEGRAL CALCULUS 

By John Haven Neelley and Joshua Irving Tracey. 

THE MONGEAN METHOD OF DESCRIPTIVE GEOME- 
TRY 
By William Henry Roever. 

DIFFERENTIAL EQUATIONS 
By Nelson B. Conkwright. 

TABLES OF INTEGRALS AND OTHER MATHEMATICAL 
DATA 
By Herbert Bristol Dwight. 

AN INTRODUCTION TO THE MATHEMATICS OF LIFE 
INSURANCE 
By Walter O. Menge and James W. Glover. 



LOGARITHMIC AND 
TRIGONOMETRIC TABLES 



REVISED EDITION 



PREPARED UNDER THE DIRECTION OF 
EARLE RAYMOND HEDRICK 



ENTIRELY RE-SET IN A NEW TYPE FACE 



NEW YORK 

THE MACMILLAN COMPANY 
1937 



Copyright, 1913 and 1920, 
By THE MACMILLAN COMPANY. 



All rights reserved — no part of this book 
may be reproduced in any form without 
permission in writing from the publisher, 
except by a reviewer who wishes to quote 
brief passages in connection with a review 
written for inclusion in magazine or 
newspaper. 



Set up and electrotyped. Revised edition published August, 1920. Reprinted 
April, 1924 ; May, September, December, 1925 ; April, June, 1926 ; January, 
July, 1927 ; March, December, 1928 ; November, 1929 ; October, November, 1930 ; 
April, October, 1931 ; February, 1932 ; April, 1933 ; May, 1933 ; November, 1933 ; 
July, 1935 ; May, 1936 ; December, 1937. 



PRINTED IN THE UNITED STATES OF AMERICA 



PREFACE 

The present edition of this book contains all of the tables in the 
previous editions. All have been reset in a new and very readable type. 

Great care has been exercised to preserve and to increase the great 
degree of reliability that existed in the previous edition. For careful 
reading of the proofs, I am indebted to my daughter Elisabeth and 
her husband, Mr. Richard L. Miller, to several of my own students, 
and to the following friends in other institutions, sometimes with the 
aid of their students : Professor C. H. Currier, Brown University ; Pro- 
fessor H. T. Davis, University of Indiana; Professor H. B. Dwight, 
Massachusetts Institute of Technology; Professor W. B. Ford, Uni- 
versity of Michigan ; Professor A. M. Harding, University of Arkansas ; 
Professor C. G. Jaeger, Pomona College ; Professors H. W. Kuhn and 
J. H. Weaver, Ohio State University; Professor L. S. Johnston, Uni- 
versity of Detroit; Professors A. J. Kempner and C. A. Hutchinson, 
University of Colorado; Professor G. W. Mullins, Barnard College 
(Columbia University) ; Professor L. M. Passano, Massachusetts Insti- 
tute of Technology; Professors H. L. Rietz, Roscoe Woods, and J. F. 
Reilly, University of Iowa; Professor E. E. Watson, Iowa State Teachers 
College at Cedar Falls; Dr. E. W. Wilson, Cambridge, Mass.; and Pro- 
fessor Kathryn Wyant, Athens College, Athens, Alabama. Each of 
these persons or groups has read the complete proof. With deep feeling, 
I may record also that the late Professor Louis Ingold of the University 
of Missouri read the proofs up to page 54, and had sent me the last of 
these pages within a week of his sudden death on January 25, 1935. 

These careful readings render the possibility of printers' errors ex- 
tremely remote. While the calculation of the probability that an 
undiscovered error exists is not simple, a strict account has been kept of 
each error found and of the total number not found by any one group of 
readers, so that a basis for a statistical calculation is known: the result- 
ing probability that even one undiscovered printers' error exists is not 
more than one in many thousands. 

I desire to express here my thanks to all those, particularly those 
mentioned above, who have assisted in the effort to make these tables 
so free from errors and therefore so reliable. I know of no comparable 
method for securing this quality in a set of tables. 

I repeat also my acknowledgment made in the original edition to 
many previously existing tables, particularly those of Vega and those 
of Houel. During the proof-reading, those who have assisted have 
compared these tables with a great variety of existing tables, including 
several high-place tables, and the values have been recalculated and 
checked whenever a disagreement has been discovered. 

Finally, I wish to mention the excellent cooperation of the editorial 
staff of the Macmillan Company under the able direction of Mr. F. T. 
Sutphen. 

E. R. Hedrick 



CONTENTS 

Explanation of the Tables. 



PAGES 

vii-xvi 



TABLES PRINCIPALLY TO FIVE PLACES 

Table I. Common Logarithms of Numbers .... 1-19 
Table la. Condensed Logarithms and Antilogarithms . . 20 
Table II. Actual Values of the Trigonometric Functions. 21-44 
Table Ilia. Values of S and T for Interpolation ... 45 
Table III. Common Logarithms of the Trigonometric Func- 
tions 45-90 

Table IV. Reduction of Degrees to Radians .... 91 

Table V. Trigonometric Functions of Angles in Radians . 92-93 

Table Va. Reduction of Radians to Degrees .... 93 

Table VI. Powers — Roots — Reciprocals 94-111 

Table VII. Napierian or Natural Logarithms .... 112-114 

Table VIII. Multiples of M and of 1/M 115 

Table IX. Values and Logarithms of Hyperbolic Functions 116-122 

Table X. Values and Logarithms of Haversines . . . 123-125 

Table XL Factor Table — Logarithms of Primes . . . 126-127 

Table Xlla. Compound Interest 128 

Table XH6. Compound Discount 129 

Table XIIc. Amount of an Annuity 130 

Table XIIc?. Present Value of an Annuity 131 

Table XHe. Logarithms for Interest Computations . . . 132 

Table Xll/. American Experience Mortality Table . . . 132 

Table XIII. Important Constants 133 

BRIEF TABLES— PRINCIPALLY TO FOUR PLACES 

Table XlVa. Common Logarithms 134-135 

Table XIV6. Antilogarithms 136-137 

Table XIVc. Values and Logarithms of Trigonometric Func- 
tions 138-142 



•vTl 



EXPLANATION OF THE TABLES 

TABLE I. FIVE-PLACE COMMON LOGARITHMS OF 
NUMBERS FROM 1 TO 10 000 



1. Common Logarithms. The power to which 10 must be raised to produce 
any number n is called the common logarithm * of n. Thus log 10 = 1, 
log 100 = 2, log 1000 = 3, etc.; log 1 = 0, log 0.1 = -1; log 0.01 = -2, 
log 0.001 = — 3, etc. In general, if 10* = n, I is called the common logarithm 
of n, and is denoted by log n. 

2. Fundamental Principles. Logarithms constitute a great labor-saving de- 
vice in arithmetical computations. The principles of their application are 
stated as follows: 

I. The logarithm of a product is equal to the sum of the logarithms of the factors: 
log ab = log a + log 6. This follows from the fact that if 10* = a and 10 1, = 6, 
10*" hL = a*b. In brief: to multiply , add logarithms. 

II. The logarithm of a fraction is equal to the difference obtained by subtracting 
the logarithm of the denominator from the logarithm of the numerator: log (a/6) 
= log a — log b. For, if 10* = a and lO 1 * = 6, then lO* -1 * = a -r o. In brief: 
to divide, subtract logarithms. 

III. The logarithm of a power is equal to the logarithm of the base multiplied 
by the exponent of the power: log a b = b log a. This follows from the fact that 
if 10* = a, then 10* 6 - a h . 

IV. The logarithm of a root of a number is found by dividing the logarithm of 
the number by the index of the root: log \a = (log a)/b. This follows from the 
fact that if 10* = a, then 10*' & - a ltb = fya. 

Corollary of II. The logarithm of the reciprocal of a number is the negative 
of the logarithm of the number: log (1/a) = —log a, since log 1 = 0. 

3. Characteristic and Mantissa. Every real positive number has a real 
common logarithm. If a and b are any two real positive numbers such that 
a < 6, then log a < log b. Neither zero nor any negative number has a real 
logarithm. 



a 


1 


10 


100 


1000 


10000 


100000 


1000000 


10000000 


log a 





1 


2 


3 


4 


5 


6 


7 



Inspection of the preceding table shows that 

the logarithm of every number between 1 and 10 is a proper fraction, 
the logarithm of every number between 10 and 100 is 1 + a fraction, 
the logarithm of every number between 100 and 1000 is 2 + a fraction; 



* Common logarithms are exponents of the base 10; other systems of logarithms have bases 
different from 10; Napierian logarithms (see Table VII, p. 112) have a base denoted by e, an 
irrational number whose value is approximately 2.71828. When it is necessary to call attention 
to the base, the expression logio n will mean common logarithm of n; log e n will mean the 
Napierian logarithm, etc.; but in this book log n denotes log 10 n unless otherwise explicitly stated. 

vii 



Vlll 



EXPLANATION OF THE TABLES 



C§3 



and so on. It is evident that the logarithm of every number (not an exact 
power of 10) consists of a whole number + a fraction (usually written as a 
decimal). The whole number is called the characteristic; the decimal is 
called the mantissa. The characteristic of the logarithm of any number 
greater than 1 may be determined as follows: 

Rule I. The characteristic of any number greater than 1 is one less than the 
number of digits before the decimal point. 

The following table shows that 



a 


.0000001 


.000001 


.00001 


.0001 


.001 


.01 


.1 


1 


log a 


-7 


-6 


-5 


-4 


-3 


-2 


-1 






the logarithm of every number between 0.1 and 1 is —1 + a fraction, 

the logarithm of every number between 0.01 and 0.1 is —2 + a fraction, 

the logarithm of every number between 0.001 and 0.01 is — 3 + a fraction; 
and so on. 

Thus the characteristic of every number between and 1 is a negative whole 
number; there is a great practical advantage, however, in computing, to 
write these characteristics as follows: —1 = 9 — 10, —2 = 8 — 10, —3 
= 7-10, etc. Thus, the logarithm of 0.562 is - 1+ 0.74974, but this should 
be written 9.74974 — 10; and similarly for all numbers less than 1. 

Rule II. The characteristic of a number less than 1 is found by subtracting 
from 9 the number of ciphers between the decimal point and the first significant digit, 
and writing —10 after the result. 

Thus, the characteristic of log 645 is 2 by Rule I; the characteristic of 
log 64.5 is 1 by (I); of log 6.45 is by (I); of log 0.645 is 9 - 10 by (II); of 
log 0.0645 is 8 - 10 by (II). 

To move the decimal point in a given number one place to the right is equiva- 
lent to adding one unit to its logarithm, because this is equivalent to multi- 
plying the given number by 10. Likewise, to move the decimal point one 
place to the left is equivalent to subtracting one unit from the logarithm. 
Hence, moving the decimal point any number of places to the right or left 
does not change the mantissa but only the characteristic* 

Thus, 5345, 5.345, 534.5, 0.05345, 534500 all have the same mantissa. 

4. Use of the Table. To use logarithms in computation we need a table 
arranged so as to enable us to find, with as little effort and time as possible, 
the logarithms of given numbers and, vice versa, to find numbers when their 
logarithms are known. Since the characteristics may be found by means of 
Rules I and II, p. viii, only mantissas are given. This is done in Table I. 
Most of the numbers in this table are irrational, and must be represented in 
the decimal system by approximations. A five-place table is one which gives 
the values correct to five places of decimals. 



* Another rule for finding the characteristic, based on this property, is often useful: if the 
decimal point were just after the first significant figure, the characteristic would be zero; start 
at this point and count the digits passed over to the left or right to the actual decimal point; 
the number obtained is the characteristic, except for sign; the sign is negative if the movement 
was to the left, positive if the movement was to the right. 



§6] COMMON LOGARITHMS ix 

Problem 1. To find the logarithm of a given number. First, determine the 
characteristic, then look in the table for the mantissa. 

To find the mantissa in the table when the given number (neglecting the 
decimal point) consists of four, or less, digits (exclusive of ciphers at the 
beginning or end), look in the column marked N for the first three digits and 
select the column headed by the fourth digit: the mantissa will be found at 
the intersection of this row and this column. Thus to find the logarithm of 
72050, observe first (Rule I) that the characteristic is 4. To find the mantissa, 
fix attention on the digits 7205; find 720 in column N, and opposite it in 
column 5 is the desired mantissa, 0.85763; hence log 72050 = 4.85763. The 
mantissa of 0.07826 is found opposite 782 in column 6 and is 0.89354; hence 
log 0.07826 = 8.89354 - 10. 

5. Interpolation. If there are more than four significant figures in the 
given number, its mantissa is not printed in the table; but it can be found 
approximately by assuming that the mantissa varies as the number varies 
in the small interval not tabulated; while this assumption is not strictly cor- 
rect, it is sufficiently accurate for use with this table. 

Thus, to find the logarithm of 72054 we observe that log 72050 = 4.85763 
and that log 72060 = 4.85769. Hence a change of 10 in the number causes 
a change of 0.00006 in the mantissa; we assume therefore that a change of 4 in 
the number will cause, approximately, a change of 0.4 X 0.00006 = 0.00002 
(dropping the sixth place) in the mantissa; and we write log 72054 = 4.85763 
+ 0.00002 = 4.85765. 

The difference between two successive values printed in the table is called 
a tabular difference (0.00006, above). The proportional part of this difference 
to be added to one of the tabular values is called the correction (0.00002, 
above), and is found by multiplying the tabular difference by the appropriate 
fraction (0.4, above). These proportional parts are usually written without the 
zeros, and are printed at the right-hand side of each page, to be used when 
mental multiplications seem uncertain. 

Example 1. Find the logarithm of 0.0012647. Opposite 126 in column 4 find 0.10175; 
the tabular difference is 34 (zeros dropped) ; 0.7 X 34 is given in the margin as 24; this correction 
added gives 0.10199 as the mantissa of 0.0012647; hence log 0.0012647 = 7.10199 - 10. 

Example 2. Find the logarithm of 1.85643. Opposite 185 in column 6 find 0.26858; tabular 
difference 23; 0.43 X 23 is given in the margin as 10; this correction added gives 0.26868 as the 
mantissa of 1.85643; hence log 1.85643 = 0.26868. 

6. Reverse Reading of the Table. Problem 2. To find the number when 
its logarithm is known* First, fixing attention on the mantissa only, find from 
the table the number having this mantissa, then place the decimal point by 
means of the two following rules: t 

Rule III. // the characteristic of the logarithm is positive (in which case the 
mantissa is not followed by —10), begin at the left, count digits one more than the 
characteristic, and place the decimal point to the right of the last digit counted. 



* The number whose logarithm is k is often called the antilogarithm of k. 

t Another convenient form of these rules is as follows: if the characteristic were zero, the 
decimal point would fall just after the first significant figure; move the decimal point one place 
to the right for each positive unit in the characteristic, one place to the left for each negative 
unit in the characteristic. 



x EXPLANATION OF THE TABLES [§ 6 

Rule IV. // the characteristic is negative (in which case the mantissa will be 
preceded by a number n and followed by —10), prefix 9 — n ciphers, and place 
the decimal point to the left of these ciphers. 

Example 1. Given log x = 1.22737, to find x. 

Since the mantissa is 22737, we look for 22 in the first column and to the right and below for 
737, which we find in column 8 opposite 168. The number is therefore 1688. Since the 
characteristic is +1, we begin at the left, count 2 places, and place the point; hence x = 16.88. 

Example 2. Given log x = 2.24912, to find x. 

This mantissa is not found in the table; in such cases we interpolate as follows: select the 
mantissa in the table next less than the given mantissa, and write down the corresponding 
number; here, 1774; the tabular difference is 25; the actual difference (found by subtracting 
the mantissa of 1774 from the given mantissa) is 17; hence the proportionality factor is 17/25 
= 0.68 or 0.7 (to the nearest tenth). Since moving the decimal point does not affect the man- 
tissa, it follows that the digits in the required number are 17747 (to five places) . The charac- 
teristic 2 directs to count 3 places from the left; hence x = 177.47. 

Rule. In general, when the given mantissa is not found in the table, write 
down four digits of the number corresponding to the mantissa in the table next less 
than the given mantissa, determine a fifth figure by dividing the actual difference 
by the tabular difference, and locate the decimal point by means of the characteristic. 

7. Cologarithms. We might add the logarithms of the factors in the nu- 
merator and from this sum subtract the logarithm of the denominator; but we 
can shorten the operation by adding the negative of the logarithm of the 
denominator instead of subtracting the logarithm itself. The negative of the 
logarithm of a number (when written in convenient form for computation) 
is called the cologarithm of the number. We may find the negative of any 
number by subtracting it from zero, and it is convenient in logarithmic compu- 
tation to write zero in the form 10.00000 — 10. Thus the negative of 2.17 is 
7.83 - 10; the negative of 1.1432 - 10 is 8.8568. Remembering that the 
cologarithm of a number is its negative we have the following rule : 

To find the cologarithm of a number begin at the left of its logarithm {including 
the characteristic) and subtract each digit from 9, except the last,* which subtract 
from 10; if the logarithm has not —10 after the mantissa, write —10 after the result; 
if the logarithm has —10 after the mantissa, do not write —10 after the result. 

By this rule the cologarithm of a number can be read directly out of the 
table without taking the trouble to write down the logarithm. Attention 
must be given not to forget the characteristic. The use of the cologarithm is 
governed by the principle: 

Adding the cologarithm is equivalent to subtracting the logarithm. 

la. CONDENSED LOGARITHMS AND ANTILOGARITHMS 

8. Method of Computing Logarithms. This table is a rearrangement of the 
condensed table given by Holiel.t From it, the logarithm of any number 
whatever may be obtained to within 5 in the fifteenth place; or to any desired 
degree of accuracy less than this. 

To illustrate the process, we shall compute log ir to nine places. Taking 
7T = 3.14159 26535 8979, we divide it by 3, the first significant digit, obtaining 

* If the logarithm ends in one or more ciphers, the last significant digit is to be understood 
here. 

t Houel, Recueil de Formules et de Tables numeriques, 3d ed. t Paris, Gauthier-Villars, 1901. 



§10] TRIGONOMETRIC FUNCTIONS xi 

7r/3 = 1.04719 755 • • • . We then divide this quotient by 1.04, etc., obtaining 

finally 

7T = 3(1.04) (1.006) (1.0009) (1.00001 52172 23). 

We can obtain the logarithm of each of the first four factors from this table. 
The logarithm of the last factor can be obtained by multiplying its decimal 
part by M = 0.43429 44819; for the error made in writing 

log (1 + x) - Mx 

is less than Mx 2 /2. We find Mx either by using the fact that the last column 
in this table gives multiples of M, or (preferably) by Table VIII, page 115. 
Adding the five logarithms just mentioned, we find 

log 7T = 0.49714 98727 4, 

which is surely correct to within 1 in the tenth place. The correct value is 
0.49714 98726 9 •••. 

The process may be applied to any other number in an analogous manner. 
Such high-place logarithms are occasionally needed in statistical work and in 
the preparation of tables. 

9. Method of Computing Antilogarithms. The condensed table of anti- 
logarithms gives eleven significant figures (ten decimal places). From it, 
the antilogarithm of any number can be computed to within 5 in the tenth 
significant digit. 

Thus, to compute the antilogarithm of .4342944819 to 8 significant figures, 
we may write 

1Q0. 43429 44819 = (10°' 4 ) (10°* 03 ) (10°' 004 ) (lO * 0002 ) (10°* 00009 ) (10°' 0000 ° 44819 ). 

The first five factors may be obtained directly from the table. The last factor 
may be calculated from the formula 10 x = 1 + (1/M)x. The error in this 
formula is less than 3 in the (2k)th decimal place if x is less than (0.1)*, where 
k > 1. 

However, a much more rapid process depends on the use of Tables I and XI 
with this table. Thus, by Table I, 10°- 43429 = 2.718, nearly. By Table XI, 
log 2.718 = 0.43424 94524 • • •. Hence 10 - 43429 "» 9 - (2.718) (10°- 00004 60295 ) 
= (2.718) (10 - 00004 )(10°- 0000050295 ). Obtaining the second factor from this 
table, and the last factor from the formula 10 x = 1 + {\jM)x, by Table VIII, 
we find 10°- 43429 **«» = 2.71828 1828; the correct value is 2.718281828459 
This process requires only two long multiplications. 

II. FIVE-PLACE TABLE OF THE ACTUAL VALUES OF THE 
TRIGONOMETRIC FUNCTIONS OF ANGLES 

10. Direct Readings. This table gives the sines, cosines, tangents, and 
cotangents of the angles from 0° to 45°; and by a simple device, indicated by 
the printing, the values of these functions for angles from 45° to 90° may be 
read directly from the same table. For angles less than 45° read down the 
page, the degrees being found at the top and the minutes on the left; for angles 
greater than 45° read up the page, the degrees being found at the bottom and 
the minutes on the right. 

To find a function of an angle (such as 15° 27'.6, for example) which does 
not reduce to an integral number of minutes, we employ the process of inter- 



xii EXPLANATION OF THE TABLES [§10 

polation. To illustrate, let us find tan 15° 27'.6. In the table we find 
tan 15° 27' = 0.27638 and tan 15° 28' = 0.27670; we know that tan 15° 27'.6 
lies between these two numbers. The process of interpolation depends on the 
assumption that between 15° 27' and 15° 28' the tangent of the angle varies 
directly as the angle; while this assumption is not strictly true, it gives an 
approximation sufficiently accurate for a five-place table. Thus we should 
assume that tan 15° 27'.5 is halfway between 0.27638 and 0.27670. We may 
state the problem as follows: An increase of V in the angle increases the tangent 
0.00032; assuming that the tangent varies as the angle, an increase of 0'.6 in the 
angle will increase the tangent by 0.6 X 0.00032 = 0.00019 (retaining only 
five places) ; hence 

tan 15° 27'.6 = 0.27638 + 0.00019 = 0.27657. 
The difference between two successive values in the table is called, as in 
Table I, the tabular difference (0.00032 above). The proportional part of the 
tabular difference which is used is called the correction (0.00019 above), and 
is found by multiplying the tabular difference by the appropriate fraction of 
the smallest unit given in the table. 

Example 1. Find sin 63° 52'.8. 

We find sin 63° 52' = 0.89777; 

tabular difference = 0.00013 (subtracted mentally from the table), 
correction = 0.8 X 0.00013 = 0.00010 (to be added). 
Hence sin 63° 52'.8 = 0.89787. 

Example 2. Find cos 65° 24'.8. 

cos 65° 24' = 0.41628; 
tabular difference = 26; 0.8 X 26 =21 
(to be subtracted because the cosine decreases as the angle increases). 
Hence cos 65° 24'.8 = 0.41607. 

Rule. To find a trigonometric function of an angle by interpolation: select 
the angle in the table which is next smaller than the given angle, and read its sine 
(cosine or tangent or cotangent as the case may be) and the tabular difference. 
Compute the correction as the proper proportional part of the tabular difference. 
In case of sines or tangents add the correction; in case of cosines or cotangents, 
subtract it. 

11. Reverse Readings. Interpolation is also used in finding the angle when 
one of its functions is given. 

Example 1. Given sin x = 0.32845, to find x. 

Looking in the table we find the sine which is next less than the given sine to be .32832, 
and this belongs to 19° 10'. Subtract the value of the sine selected from the given sine to obtain 
the actual difference = 0.00013; note that the tabular difference = 0.00027. The actual dif- 
ference divided by the tabular difference gives the correction = 13/27 = 0.5 as the decimal of a 
minute (to be added). Hence x = 19° 10'. 5. 

Example 2. Given cos x = 0.28432, to find x. 

The cosine in the table next less than this is 0.28429 and belongs to 73° 29'; the tabular dif- 
ference is 28; the actual difference is 3; correction = 3/28 = 0.1 (to be subtracted). Hence 
x = 73° 28'.9. 

Rule. To find an angle when one of its trigonometric functions is given: select 
from the table the same named function which is next less than the given function, 
noting the corresponding angle and the tabular difference; compute the actual 
difference (between the selected value of the function and the given value) and divide 



§12] TRIGONOMETRIC FUNCTIONS xiii 

it by the tabular difference; this gives the correction which is to be added if the given 
function is sine or tangent, and to be subtracted if the given function is cosine or 
cotangent 

III. FIVE-PLACE COMMON LOGARITHMS OF THE 
TRIGONOMETRIC FUNCTIONS 

12. Use of the Table. If it is required to find the numerical value of 
x = 27.85 X sin 51° 27', we may apply logarithms as follows: 

log 27.85 = 1.44483. 
log sin 51° 27' = 9.89324 - 10 (add) 

log x = 1.33807 x = 21.78 

The only new idea here is the method of finding log sin 51° 27', which means 
the logarithm of the sine of 51° 27'. The most obvious way is to find in Table II, 
sin 51° 27' = 0.78206, and then to find in Table I, log 0.78206 = 9.89324 - 10, 
but this involves consulting two tables. To avoid the necessity of doing this, 
Table III gives the logarithms of the sines, cosines, tangents, and cotangents. 
The arrangement and the principles of interpolation are similar to those given 
on p. vii for Table I. The sines and cosines of all acute angles, the tangents 
of all acute angles less than 45° and the cotangents of all acute angles greater 
than 45° are proper fractions, and their logarithms end with —10, which is 
not printed in the table, but which should be written down whenever such a 
logarithm is used. 

In the printed table, values are stated so that 10 should be subtracted in every case. 

Example 1. Find log sin 68° 25'. 4. 

On the page having 68° at the bottom, and in the row having 25' on the right find log sin 
68° 25' = 9.96843 — 10; the tabular difference is 5; 0.4 X 5 is given in the margin as 2; this is 
the correction to be added, giving log sin 68° 25'.4 = 9.96845 - 10. 

(In case of sine and tangent add the correction. In case of cosine and cotangent, subtract 
the correction.) 

Example 2. Given log cos x = 9.72581 — 10, to find x. 

The logarithmic cosine next less than the given one is 9.72562 — 10 and belongs to 57° 53'; 
the actual difference is 19; the tabular difference is 20; hence the correction is 19/20 =1.0 
(to the nearest tenth) ; (subtract) ; hence x = 57° 52'.0. 

In finding log ctn a. for any angle a, note that log ctn a. — —log tan a, since 
ctn a = 1/tan <x. Hence the tabular differences for log ctn are precisely the same 
as those for log tan throughout the table, but taken in reversed order. Likewise, 
log sec a. = —log cos a, log esc a = —log sin a; hence the values of log sec a. 
and log esc a. are omitted. 

For angles near 0° or near 90°, the interpolations are not very accurate if 
the differences are large. For the calculation of sine or tangent near 0°, 
Table Ilia, page 45, gives the values of 

S = log sin A — log A' and T = log tan A — log A', 
where A is the given angle and A' is the number of minutes in A, for values of 
A between 0° and 3°. Then 

log sin A = log A' + S and log tan A = log A' + T, 
for small angles. Moreover, since we have cos A = sin (90° — A) and 
ctn A = tan (90° - A), 



xiv EXPLANATION OF THE TABLES [§ 12 

log cos A = log (90° - A)' +S and log ctn A = log (90° - A)' + T, 

when A is near 90°. 

Another method practically equivalent to the preceding is to use the ap- 
proximate relations 

log sin A — log sin B = log A' — log B' 
and 

log tan A — log tan B = log A' — log B\ 

where A is the given angle and B is the nearest angle to A that is given in the 
table. If A < 3° and | A — B \ < 1', these formulas give log sin A and 
log tan A to five decimal places. 

IV-V. RADIAN MEASURE 

13. Computations in Radian Measure. The reduction of degrees to radians 
is facilitated by Table IV — Conversion of Degrees to Radians. Since x radians 
= 180°, this table may be regarded as a table of multiples of 7r/180. 

The values of sin x, cos x, tan x, are stated for every angle x from 0.00 
to 1.60 radians at intervals of 0.01 radian in Table V — Trigonometric 
Functions in Radian Measure. The values of any of these functions for larger 
values of x may be computed by first converting the value of the angle in 
radian measure to degree measure, by Table Va, and then finding the value 
of the function from Table II. 

The reduction of radians to degrees can be performed directly by Table V; 
or, for greater accuracy, by the supplementary Table Va. 

VI. POWERS— ROOTS— RECIPROCALS 

14. Arrangement. This table is arranged so that the square, cube, square 
root, cube root, or reciprocal can be read directly to five decimal places for 
any number n of three significant figures. To attain this, not only n 2 , n 3 , Vw» 
Vn, 1/n, but also VlOn, \^10 n, "v'lOOn are printed on every page. All values 
have been carefully recomputed and checked. 

Thus t o fin d Vl.17, read in Vn column the result: 1.08167. To find Vll.7, read in the same 
line, in VlO n colu mn t he result: 3.42053. To find Vll7, read 10 times the entry in Vn column, 
since Vll7 = 10 VI7l7. 

Similarly, \1.17 = 1.05373 from yfn column; ^11.7 = 2.27019 from the same line in -^10 n 
column; ^IY7 = 4.89097 from the same line in -\Jl00 n column. 

The effect of a change in the decimal point in n 2 , n 3 , and 1/n is only to shift 
the decimal point in the result, without altering the digits printed. 

VII. NAPIERIAN OR NATURAL LOGARITHMS 

15. The Base e. — Natural Logarithms. The number e = 2.7182818 • • • 
is called the natural base of logarithms. The logarithms of numbers to this 
base are given in Table VII at intervals of 0.01 from 0.01 to 10.09, and at unit 
intervals from 10 to 409. The fundamental relation log e n = log e 10 X logio n 
enables us to transfer from the base 10 to the base e, or conversely; where 
loge 10 = 2.30258509 •••. 



§ 19] OTHER TABLES XV 

VIII. MULTIPLES OF M AND OF 1/ilf 

16. Multiples of M and 1/M. This table is convenient whenever a number 
is to be multiplied by M or by 1/ilf. This occurs whenever it is desired to 
change from common logarithms to natural logarithms, or conversely, since 
M = log 10 e and since we have 

log™ x = (loge #) (logio e) = M loge x and log e x — (1/M) log™ x. 
Other formulas that require these multiples are 

logio e x = x logio e = x-M and log e (10 n -a;) = log e x + n(l/M); 
and the approximate formulas (see §§8, 9, pp. x, xi) 

logio (1 =fc x) - ±x-M and 10=^ = 1 ± (1/M)z. 

IX. VALUES AND LOGARITHMS OF HYPERBOLIC FUNCTIONS 

17. Hyperbolic Functions. This table gives the values of e*, e" x , sinh x, 
cosh x, tanh #; and the logarithms of e x , sinh z, cosh x, at varying intervals 
from x = to x — 10. It is to be noted that log e~ x = — log e x and log tanh x 
= log sinh x — log cosh x. The table may be extended indefinitely by 
means of Table VIII, since logio e x = x* M; for this reason Table VIII may be 
regarded as a table of values of logio e*. 

X. VALUES AND LOGARITHMS OF HAVERSINES 

18. Haversines. This table gives the values and the logarithms of the 
haversines of angles from 0° to 180° at intervals of 10'. The haversine, which 
means half of the versed sine, is 

hav A = (J^) vers A = (3^)(1 — cos A); 
hence its values to five places may be computed from the table of cosines. 
It is used extensively in navigation, and it may be used to advantage in the 
solution of ordinary oblique triangles. 

XI. FACTOR TABLE—LOGARITHMS OF PRIMES 

19. Factors of Composite Numbers. Logarithms of Primes. The uses 
of this table are evident in questions involving factoring, and for finding high- 
place logarithms of numbers whose prime factors are less than 2018. 

We shall illustrate the finding of logarithms of other numbers by finding 
log 7T. Taking x = 3.14159 26536, divide by 3 (the first digit), obtaining 
1.04719 75512 •••. Divide this quotient by 1.047 (in general, by the nearest 
first four digits), obtaining 1.00018 8683 • • • . By Table VIII, the approxi- 
mate formula log (1 ± x) = ±X'M gives 

log 1.00018 8683 = 0.00008 1944 (Table VIII) 

log 3 = 0.47712 12547 (Table XI) 

log 1.047 = log 3 + log 0.349 = 0.01994 66817 (Table XI) 

log ir = 0.49714 9880 

while the true value of log x is 0.49714 98726 9, so that the error is less than 1 in 
the eighth place. In general, this process will give the logarithm of any number 
to within 6 in the eighth decimal place, and the probable error is less than 1.5 
in the eighth place. For still greater accuracy, see Table la and § 10. 



XVI 



EXPLANATION OF THE TABLES 



[§20 



XII. INTEREST TABLES 

20. Interest Tables. Tables XII a, 6, c, d give compound interest and 
annuity data for various per cents up to fifty years. Aside from the obvious 
uses, formulas involving these data will be found in works on statistics, ac- 
counting, and the mathematics of business. 

Table XHe gives the logarithms of (1 + r) to fifteen places, for all ordinary 
values of r from J^% to 10%. For other values of r, log (1 -f r) may be 
computed from Table la (see § 8). The final result in interest calculations 
may be obtained to nine significant figures by the antilogarithms of Table la 
(see § 9). 

Table XII/ is the American Experience Mortality Table. 

XIV. FOUR-PLACE TABLES 

21. Four-place Tables. These are duplicates of the preceding five-place 
tables, reduced to four places, and with larger intervals between the tabulations. 
The value of such four-place tables consists in the greater speed with which 
they can be used, in case the degree of accuracy they afford is sufficient for 
the purpose in hand. 

XlVa. Logarithms of Numbers. The only special feature of this table 
is that the 'proportional parts are printed for every tenth in every row; hence the 
logarithm of any number of four significant figures can be read directly. 

XIV6. Antilogarithms. This table will be found to facilitate approximate 
calculations to a marked degree. The proportional parts are stated in the 
right-hand margin for each row separately. This arrangement, with the 
corresponding one in Table XlVa, makes the tables effectively four-place each 
way. 

XIVc. Values and Logarithms of Trigonometric Functions. In this table, 
the values of sin a, cos a, tan a, ctn a, and their common logarithms, are stated 
for each 10-minute interval in a. The characteristics of the logarithms are 
omitted, since they can be supplied readily from the value. 





Greek Alphabet 






Letters Names 


Letters Names 


Letters 


Names 


Letters Names 


A a Alpha 


H 77 Eta 


N v 


Nu 


T r Tau 


B £ Beta 


6 Theta 


E £ 


Xi 


T v Upsilon 


T 7 Gamma 


I i Iota 


o 


Omicron 


3> <f> Phi 


A 5 Delta 


K k Kappa 


n 7T 


Pi 


X x Chi 


E e Epsilon 


A X Lambda 


p p 


Rho 


^ y}/ Psi 


Z f Zeta 


M /X Mu 


2 as 


Sigma 


12 w Omega 



LOGARITHMIC AND 
TRIGONOMETRIC TABLES 

TABLE I 
COMMON LOGARITHMS OF NUMBERS 

FROM 

1 TO 10 000 

TO 

FIVE DECIMAL PLACES 











1 


— 100 










N 


Log 


N 


Log 


N 


Log 


N 


Log 


N 


Log 




1 
2 
3 

4 
5 
6 

7 
8 
9 




20 


1.30 103 


40 


1.60 206 


60 


1.77 815 


80 


1.90 309 




0.00 000 
0.30 103 
0.47 712 

0.60 206 
0.69 897 
0.77 815 

0.84 510 
0.90 309 
0.95 424 


21 
22 
23 

24 
25 
26 

27 

28 
29 


1.32 222 
1.34 242 
1.36 173 

1.38 021 

1.39 794 
1.41 497 

1.43 136 

1.44 716 
1.46 240 


41 
42 
43 

44 
45 

46 

47 
48 
49 


1.61 278 

1.62 325 

1.63 347 

1.64 345 

1.65 321 

1.66 276 

1.67 210 

1.68 124 

1.69 020 


61 
62 
63 

64 
65 
66 

67 
68 
69 


1.78 533 

1.79 239 

1.79 934 

1.80 618 

1.81 291 

1.81 954 

1.82 607 

1.83 251 
1.83 885 


81 

82 
83 

84 
85 
86 

87 
88 
89 


1.90 849 

1.91 381 

1.91 908 

1.92 428 

1.92 942 

1.93 450 

1.93 952 

1.94 448 
1.94 939 


10 


1.00 000 


30 


1.47 712 


50 


1.69 897 


70 


1.84 510 


90 


1.95 424 


11 
12 
13 

14 
15 
16 

17 
18 
19 


1.04 139 
1.07 918 
1.11 394 

1.14 613 
1.17 609 
1.20 412 

1.23 045 
1.25 527 
1.27 875 


31 
32 
33 

34 
35 
36 

37 

38 
39 


1.49 136 

1.50 515 

1.51 851 

1.53 148 

1.54 407 

1.55 630 

1.56 820 

1.57 978 
1.59 106 


51 
52 
53 

54 
55 

56 

57 

58 
59 


1.70 757 

1.71 600 

1.72 428 

1.73 239 

1.74 036 

1.74 819 

1.75 587 

1.76 343 

1.77 085 


71 
72 
73 

74 
75 
76 

77 
78 
79 


1.85 126 

1.85 733 

1.86 332 

1.86 923 

1.87 506 

1.88 081 

1.88 649 

1.89 209 
1.89 763 


91 
92 
93 

94 
95 
96 

97 
98 
99 


1.95 904 

1.96 379 

1.96 848 

1.97 313 

1.97 772 

1.98 227 

1.98 677 

1.99 123 
1.99 564 


N 


Log 


N 


Log 


N 


Log 


N 


Log 


N 


Log 



2 




100 — 


Logarithms of Numbers — 


■150 








d 


N. 





l 


2 


3 


4 


5 


6 


7 


'8 


9 


Prop. Pts. 


100 


00 000 


043 


087 


130 


173 


217 


260 


303 


346 


389 




101 
102 
103 

104 
105 
106 

107 
108 
109 


432 

860 

01284 

703 

02 119 
531 

938 

03 342 
743 


475 
903 
326 

745 
160 
572 

979 
383 

782 


518 
945 
368 

787 
202 
612 

*019 
423 

822 


561 

988 
410 

828 
243 
653 

*060 
463 
862 


604 

*030 

452 

870 

284 
694 

*100 
503 
902 


647 

*072 

494 

912 
325 

735 

*141 
543 
941 


689 

*115 

536 

953 
366 

776 

*181 
583 
981 


732 

*157 
578 

995 
407 
816 

*222 

623 

*021 


775 

*199 

620 

*036 
449 

857 

*262 

663 

*060 


817 

*242 

662 

*078 
490 
898 

*302 

703 

*100 


1 
2 
3 

4 
5 
6 
7 
8 
9 


44 

4.4 
8.8 
13.2 
17.6 
22.0 
26.4 
30.8 
35.2 
39.6 


43 

4.3 
8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 


42 

4.2 
8.4 
12.6 
16.8 
21.0 
25.2 
29.4 
33.6 
37.8 


110 


04 139 


179 


218 


258 


297 


336 


376 


415 


454 


493 




111 
112 
113 

114 
115 
116 

117 
118 
119 


532 
922 

05 308 

690 

06 070 
446 

819 

07188 

555 


571 
961 
346 

729 

108 
483 

856 
225 
591 


610 
999 
385 

767 
145 
521 

893 
262 
628 


650 

*038 

423 

805 
183 

558 

930 

298 
664 


689 

*077 

461 

843 
221 
595 

967 
335 
700 


727 

*115 

500 

881 
258 
633 

*004 
372 
737 


766 

*154 

538 

918 
296 
670 

*041 
408 
773 


805 

*192 

576 

956 
333 

707 

*078 
445 
809 


844 

*231 

614 

994 
371 

744 

*115 

482 
846 


883 

*269 

652 

*032 
408 
781 

*151 
518 

882 


1 
2 
3 
4 
5 
6 
7 
8 
9 


41 

4.1 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 


4U 

4.0 
8.0 
12.0 
16.0 
20.0 
24.0 
28.0 
32.0 
36.0 


ay 

3.9 

7.8 
11.7 
15.6 
19.5 
23.4 
27.3 
31.2 
35.1 

36 

3.6 
7.2 

10.8 
14.4 
18.0 
21.6 
25.2 
28.8 
32.4 


120 


918 


954 


990 


*027 


*063 


*099 


*135 


*171 


*207 


*243 




121 
122 
123 

124 
125 
126 

127 
128 
129 


08 279 
636 
991 

09 342 
691 

10 037 

380 

721 

11059 


314 

672 

*026 

377 
726 
072 

415 
755 
093 


350 

707 

*061 

412 
760 
106 

449 
789 
126 


386 

743 

*096 

447 
795 
140 

483 
823 
160 


422 

778 

*132 

482 
830 
175 

517 
857 
193 


458 

814 

*167 

517 
864 
209 

551 

890 
227 


493 

849 
*202 

552 

899 
243 

585 
924 
261 


529 

884 
*237 

587 
934 

278 

619 
958 
294 


565 
920 

*272 

621 
968 
312 

653 

992 
327 


600 

955 

*307 

656 

*003 
346 

687 

*025 

361 


1 
2 
3 
4 
5 
6 
7 
8 
9 


38 

3.8 

7.6 
11.4 
15.2 
19.0 
22.8 
26.6 
30.4 
34.2 


37 

3.7 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
29.6 
33.3 


130 


394 


428 


461 


494 


528 


561 


594 


628 


661 


694 




131 
132 
133 

134 
135 
136 

137 

138 
139 


727 

12 057 
385 

710 

13 033 
354 

672 

988 

14 301 


760 
090 
418 

743 

066 
386 

704 

*019 

333 


793 
123 
450 

,775 
098 
418 

735 

*051 
364 


826 
156 
483 

808 
130 
450 

767 

*082 

395 


860 
189 
516 

840 
162 

481 

799 

*114 

426 


893 
222 
548 

872 
194 
513 

830 

*145 

457 


926 
254 
581 

905 
226 
545 

862 

*176 

489 


959 

287 
613 

937 
258 

577 

893 

*208 

520 


992 
320 
646 

969 
290 
609 

925 

*239 

551 


*024 
352 

678 

*001 
322 
640 

956 

*270 

582 


1 
2 
3 
4 
5 
6 
7 
8 
9 


3!> 

3.5 

7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 


34 

3.4 

6.8 
10.2 
13.6 
17.0 
20.4 
23.8 
27.2 
30.6 


33 

3.3 
6.6 
9.9 
13.2 
16.5 
19.8 
23.1 
26.4 
29.7 


140 


613 


644 


675 


706 


737 


768 


799 


829 


860 


891 




141 
142 
143 

144 
145 
146 

147 
148 
149 


922 

15 229 
534 

836 

16 137 
435 

732 

17 026 
319 


953 
259 
564 

866 
167 
465 

761 
056 
348 


983 
290 
594 

897 
197 
495 

791 
085 
377 


*014 
320 
625 

927 
227 
524 

820 
114 
406 


*045 
351 
655 

957 
256 
554 

850 
143 
435 


*076 
381 
685 

987 
286 

584 

879 : 

173 

464 


*106 
412 
715 

*017 
316 
613 

909 
202 
493 


*137 
442 
746 

*047 
346 
643 

938 
231 
522 


*168 
473 
776 

*077 
376 
673 

967 
260 
551 


*198 
503 
806 

*107 
406 
702 

997 
289 
580 


1 
2 
3 
4 
5 
6 
7 
8 
9 


32 

3.2 
6.4 
9.6 
12.8 
16.0 
19.2 
22.4 
25.6 
28.8 


31 

3.1 
6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 


30 

3.0 
6.0 
9.0 
12.0 
15.0 
18.0 
21.0 
24.0 
27.0 


150 


609 


638 


667 


696 


725 


754 


782 


Sll 


840 


869 




N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




150 — 


Logarithms of Numbers — 


200 






3 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


150 


17 609 


638 


667 


696 


725 


754 


782 


811 


840 


869 




151 
152 
153 

154 
155 
156 

157 
158 
159 


898 

18 184 
469 

752 

19 033 
312 

590 
866 

20 140 


926 
213 
498 

780 
061 
340 

618 
893 
167 


955 
241 
526 

808 
089 
368 

645 
921 
194 


984 
270 
554 

837 
117 
396 

673 
948 
222 


*013 
298 
583 

865 
145 
424 

700 
976 

249 


*041 
327 
611 

893 
173 
451 

728 

*003 

276 


*070 
355 
639 

921 

201 
479 

756 

*030 
303 


*099 
384 
667 

949 
229 
507 

783 

*058 

330 


*127 
412 
696 

977 
257 
535 

811 

*085 

358 


*156 
441 
724 

*005 

285 
562 

838 

*112 

385 


1 
2 
3 
4 
5 
6 
7 
8 
9 


29 

2.9 

5.8 
8.7 
11.6 
14.5 
17.4 
20.3 
23.2 
26.1 


28 

2.8 
5.6 
8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 


160 


412 


439 


466 


493 


520 


548 


575 


602 


629 


656 




161 
162 
163 

164 
165 
166 

167 
168 
169 

170 

171 
172 
173 

174 
175 
176 

177 
178 
179 

180 


683 

952 

21219 

484 

748 

22 011 

272 
531 

789 


710 
978 
245 

511 

775 
037 

298 
557 
814 


737 
*005 

272 

537 
801 
063 

324 
583 

840 


763 

*032 

299 

564 

827 
089 

350 

608 
866 


790 

*059 

325 

590 
854 
115 

376 
634 
891 


817 

*085 

352 

617 
880 
141 

401 
660 
917 


844 
*112 

378 

643 
906 
167 

427 
686 
943 


871 

*139 

405 

669 
932 
194 

453 

712 
968 


898 

*165 

431 

696 
958 
220 

479 

737 
994 


925 

*192 

458 

722 
985 
246 

505 

763 

*019 


1 

2 
3 
4 
5 
6 
7 
8 
9 


27 

2.7 
5.4 
8.1 
10.8 
13.5 
16.2 
18,9 
21.6 
24.3 


26 

2.6 
5.2 

7.8 
10.4 
13.0 
15.6 
18.2 
20.8 
23.4 


23 045 


070 


096 


121 


147 


172 


198 


223 


249 


274 




300 
553 
805 

24 055 
304 
551 

797 

25 042 
285 


325 

578 
830 

080 
329 
576 

822 
066 
310 


350 
603 
855 

105 
353 
601 

846 
091 
334 


376 
629 
880 

130 

378 
625 

871 
115 
358 


401 
654 
905 

155 
403 
650 

895 
139 

382 


426 
679 
930 

180 
428 
674 

920 
164 
406 


452 
704 
955 

204 
452 
699 

944 
188 
431 


477 
729 
980 

229 
477 
724 

969 
212 
455 


502 

754 

*005 

254 

502 

748 

993 
237 
479 


528 

779 

*030 

279 
527 
773 

*018 
261 
503 


1 

2 
3 
4 
5 
6 
7 
8 
9 


2o 

2.5 

5.0 
7.5 
10.0 
12.5 
15.0 
17.5 
20.0 
22.5 


24 

2.4 

4.8 
7.2 
9.6 
12.0 
14.4 
16.8 
19.2 
21.6 


527 


551 


575 


600 


624 


648 


672 


696 


720 


744 




181 
182 
183 

184 
185 
186 

187 
188 
189 

190 

191 
192 
193 

194 
195 
196 

197 
198 
199 


768 

26 007 

245 

482 
717 
951 

27184 
416 
646 


792 
031 
269 

505 
741 
975 

207 
439 
669 


816 
055 
293 

529 

764 
998 

231 
462 
692 


840 
079 
316 

553 

788 
*021 

254 

485 
715 


864 
102 
340 

576 

811 
*045 

277 
508 
738 


888 
126 
364 

600 

834 

*068 

300 
531 
761 


912 
150 
387 

623 

858 
*091 

323 
554 

784 


935 
174 
411 

647 

881 

*114 

346 

577 
807 


959 
198 
435 

670- 
905 
*138 

370 
600 
830 


983 
221 

458 

-694 

928 

*161 

393 
623 

852 


1 
2 
3 
4 
5 
6 
7 
8 
9 


23 

2.3 

4.6 
6.9 
9.2 
11.5 
13.8 
16.1 
18.4 
20.7 


22 

2.2 

4.4 
6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 


875 


898 


921 


944 


967 


989 


*012 


*035 


*058 


*081 




28 103 
330 
556 

780 

29 003 
226 

447 
667 

885 


126 
353 

578 

803 
026 

248 

469 

688 
907 


149 
375 
601 

825 
048 
270 

491 

710 
929 


171 
398 
623 

847 
070 
292 

513 
732 
951 


194 
421 
646 

870 
092 
314 

535 
754 
973 


217 
443 
668 

892 
115 
336 

557 
776 
994 


240 
466 
691 

914 
137 
358 

579 

798, 
*016 


262 
488 
713 

937 
159 
380 

601 

820 

*038 


285 
511 
735 

959 
181 
403 

623 

842 
*060 


307 
533 

758 

981 
203 
425 

645 

863 
*081 


1 
2 
3 

4 
5 
6 

7 
8 
9 


21 

2.1 

4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
18.9 


200 


30 103 


125 


146 


168 


190 


211 


233 


255 


276 


298 




N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



4 




200 — 


Logarithms of Numbers — 


250 






[I 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


200 


30 103 


125 


146 


168 


190 


211 


233 


255 


276 


298 




201 
202 
203 

204 
205 
206 

207 
208 
209 

210 


320 
535 
750 

963 

31 175 
387 

597 
806 

32 015 


341 
557 
771 

984 
197 
408 

618 

827 
035 


363 
578 
792 

*006 
218 
429 

639 

848 
056 


384 
600 
814 

*027 
239 
450 

660 

869 
077 


406 
621 
835 

*048 
260 
471 

681 
890 
098 


428 
643 
856 

*069 
281 
492 

702 
911 
118 


449 
664 

878 

*091 
302 
513 

723 
931 
139 


471 

685 
899 

*112 
323 
534 

744 
952 
160 


492 
707 
920 

*133 
345 
555 

765 
973 

181 


514 
728 
942 

*154 
366 
576 

785 
994 
201 


log 2 
= .30102 99957 

22 21 

1 2.2 2.1 

2 4.4 4.2 

3 6.6 6.3 

4 8.8 8.4 

5 11.0 10.5 

6 13.2 12.6 

7 15.4 14.7 

8 17.6 16.8 

9 19.8 18.9 


222 


243 


263 


284 


305 


325 


346 


366 


387 


408 

613 

818 
*021 

224 
425 
626 

826 

*025 

223 


211 
212 
213 

214 
215 
216 

217 

218 
219 


428 
634 
838 

33 041 
244 
445 

646 
846 

34 044 


449 
654 

858 

062 
264 
465 

666 
866 
064 


469 
675 
879 

082 

284 
486 

686 

885 
084 


490 
695 
899 

102 
304 
506 

706 
905 
104 


510 
715 
919 

122 
325 
526 

726 
925 
124 


531 
736 
940 

143 
345 
546 

746 
945 
143 


552 
756 
960 

163 
365 
566 

766 
965 
163 


572 

777 
980 

183 
385 
586 

786 
985 
183 


593 

797 

*001 

203 
405 
606 

806 

*005 

203 


220 


242 


262 


282 


301 


321 


341 


361 


380 


400 


420 




221 
222 
223 

224 
225 

226 

227 

228 
229 


439 
635 
830 

35 025 

218 
411 

603 
793 

984 


459 
655 
850 

044 
238 
430 

622 

813 

*003 


479 
674 
869 

064 
257 
449 

641 

832 

*021 


498 
694 
889 

083 

276 

468 

660 

851 

*040 


518 
713 
908 

102 
295 

488 

679 

870 

*059 


537 
733 
928 

122 
315 
507 

698 

889 

*078 


557 
753 
947 

141 
334 
526 

717 

908 
*097 


577 
772 
967 

160 
353 
545 

736 

927 

*116 


596 
792 
986 

180 
372 
564 

755 

946 
*135 


616 

811 

*005 

199 
392 
583 

774 

965 

*154 


1 
2 
3 

4 
5 
6 

7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 


20 

2.0 

4.0 

6.0 

8.0 

10.0 

12.0 

14.0 

16.0 

18.0 

18 

1.8 

3.6 

5.4 

7.2 

9.0 

10.8 

12.6 

14.4 

16.2 


19 

1.9 

3.8 

5.7 

7.6 

9.5 

11.4 

13.3 

15.2 

17.1 

17 

1.7 
3.4 
5.1 

6.8 
8.5 
10.2 
11.9 
13.6 
15.3 


230 


36 173 


192 


211 


229 


248 


267 


286 


305 


324 


342 


231 
232 
233 

234 
235 
236 

237 

238 
239 

240 


361 
549 
736 

922 

37 107 

291 

475 
658 
840 


380 
568 
754 

940 
125 
310 

493 
676 

858 


399 
586 
773 

959 
144 
328 

511 

694 

876 


418 
605 
791 

977 
162 
346 

530 
712 

894 


436 
624 
810 

996 
181 
365 

548 
731 
912 


455 
642 
829 

*014 
199 
383 

566 
749 
931 


474 
661 

847 

*033 

218 
401 

585 

767 
949 


493 
680 
866 

*051 
236 
420 

603 

785 
967 


511 
698 

884 

*070 
254 

438 

621 
803 
985 


530 
717 
903 

*088 
273 
457 

639 

822 
*003 


38 021 


039 


057 


075 


093 


112 


130 


148 


166 


184 


241 
242 
243 

244 
245 
246 

247 
248 
249 


202 
382 
561 

739 

917 

39 094 

270 
445 
620 


220 
399 

578 

757 
934 
111 

287 
463 
637 


238 
417 
596 

775 
952 
129 

305 
480 
655 


256 
435 
614 

792 
970 
146 

322 

498 
672 


274 
453 
632 

810 
987 
164 

340 
515 
690 


292 
471 
650 

828 

*005 

182 

358 
533 

707 


310 
489 
668 

846 

*023 

199 

375 
550 

724 


328 
507 
686 

863 

*041 

217 

393 

568 
742 


346 
525 
703 

881 

*058 

235 

410 
585 
759 


364 
543 
721 

899 

*076 

252 

428 
602 

777 


250 


794 


811 


829 


846 


863 


881 


898 


915 


933 


950 




N. 


° 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




250 — 


Logarithms of Numbers — 


300 






5 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


250 


39 794 


811 


829 


846 


863 


881 


898 


915 


933 


950 




251 
252 
253 


967 

40 140 

312 


985 
157 
329 


*002 
175 
346 


*019 
192 
364 


*037 
209 
381 


*054 
226 
398 


*071 
243 
415 


*088 
261 
432 


*106 

278 
449 


*123 
295 
466 


254 
255 
256 


483 
654 

824 


500 
671 
841 


518 

688 
858 


535 

705 

875 


552 

722 
892 


569 
739 
909 


586 
756 
926 


603 
773 
943 


620 
790 
960 


637 
807 
976 


1 
2 
3 

4 
5 

6 
7 
8 
9 


18 

1.8 

3.6 

5.4 

7.2 

9.0 

10.8 

12.6 

14.4 

16.2 


17 

1.7 

3.4 

5.1 

6.8 

8.5 

10.2 

11.9 

13.6 

15.3 


257 

258 
259 

260 


993 

41 162 

330 


*010 
179 
347 


*027 
196 
363 


*044 
212 
380 


*061 
229 
397 


*078 
246 
414 


*095 
263 
430 


*111 

280 
447 


*128 
296 
464 


*145 

313 

481 


497 


514 


531 


547 


564 


581 


597 


614 


631 


647 


261 
262 
263 


664 
830 
996 


681 

847 

*012 


697 

863 

*029 


714 

880 

*045 


731 

896 
*062 


747 

913 

*078 


764 

929 

*095 


780 

946 

*111 


797 

963 

*127 


814 

979 

*144 


264 
265 
266 


42 160 
325 

488 


177 
341 
504 


193 
357 
521 


210 
374 
537 


226 
390 
553 


243 
406 
570 


259 
423 

586 


275 

439 
602 


292 
455 
619 


308 
472 
635 




267 
268 
269 


651 
813 
975 


667 
830 
991 


684 

846 

*008 


700 

862 

*024 


716 

878 

*040 


732 

894 
*056 


749 

911 

*072 


765 

927 

*088 


781 

943 

*104 


797 

959 

*120 


M 
=log 10 e 
=log 10 2.718- • • 
=.43429 44819 


270 


43 136 


152 


169 


185 


201 


217 


233 


249 


265 


281 


271 
272 
273 


297 
457 
616 


313 
473 
632 


329 
489 
648 


345 
505 
664 


361 
521 
680 


377 
537 
696 


393 
553 
712 


409 
569 

727 


425 

584 
743 


441 
600 
759 


274 
275 
276 


775 

933 

44 091 


791 
949 
107 


807 
965 
122 


823 
981 
138 


838 
996 
154 


854 

*012 

170 


870 

*028 

185 


886 

*044 

201 


902 

*059 

217 


917 

*075 
232 


1 


16 

1.6 


15 
1.5 


277 
278 
279 


248 
404 
560 


264 
420 
576 


279 
436 
592 


295 
451 
607 


311 
467 
623 


326 

483 
638 


342 
498 
654 


358 
514 

669 


373 

529 
685 


389 
545 
700 


2 
3 

4 
5 
3 

7 
8 
9 


3.2 

4.8 

6.4 

8.0 

9.6 

11.2 

12.8 

14.4 


3.0 

4.5 

6.0 

7.5 

9.0 

10.5 

12.0 

13.5 


280 


716 


731 


747 


762 


778 


793 


809 


824 


840 


855 


281 

282 
283 


871 

45 025 

179 


886 
040 
194 


902 
056 
209 


917 
071 
225 


932 
086 
240 


948 
102 
255, 


963 
117 
271 


979 
133 

286 


994 
148 
301 


*010 
163 
317 


284 

285 
286 


332 

484 
637 


347 
500 
652 


362 
515 
667 


378 
530 

682 


393 
545 
697 


408 
561 
712 


423 

576 

728 


439 
591 
743 


454 
606 

758 


469 
621 
773 




287 
288 
289 


788 

939 

46 090 


803 
954 
105 


818 
969 
120 


834 
984 
135 


849 

*000 

150 


864 

*015 

165 


879 

*030 

180 


894 

*045 

195 


909 

*060 

210 


924 

*075 

225 


1 
2 
3 
4 
5 


14 

1.4 

2.8 
4.2 
56 
7.0 

8.4 


290 

291 
292 
293 


240 


255 


270 


285 


300 


315 


330 


345 


359 


374 


389 
538 

687 


404 
553 

702 


419 
568 
716 


434 
583 
731 


449 
598 
746 


464 
613 
761 


479 
627 

776 


494 
642 
790 


509 
657 
805 


523 
672 
820 


294 
295 
296 


835 

982 
47129 


850 
997 
144 


864 

*012 

159 


879 

*026 

173 


894 
*041 

188 


909 

*056 

202 


923 

*070 
217 


938 

*085 

232 


953 

*100 
246 


967 

*114 

261 


7 
8 
9 


9.8 
11.2 
12.6 


297 
298 
299 

300 


276 
422 
567 


290 
436 

582 


305 
451 
596 


319 
465 
611 


334 

480 
625 


349 
494 
640 


363 
509 
654 


378 
524 
669 


392 
538 
683 


407 
553 

698 




712 


727 


741 


756 


770 


784 


799 


813 


828 


842 


N. 


° 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



6 



300 — Logarithms of Numbers — 350 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop, Pts. 


300 


47 712 


727 


741 


756 


770 


784 


799 


813 


828 


842 


log 3 
==.47712 12547 

log 7T 

=.49714 98727 


301 
302 
303 

304 
305 
306 

307 
308 
309 


857 

48 001 

144 

287 
430 
572 

714 
855 
996 


871 
015 
159 

302 
444 
586 

728 

869 

*010 


885 
029 
173 

316 

458 
601 

742 

883 

*024 


900 
044 

187 

330 
473 
615 

756 

897 

*038 


914 
058 
202 

344 

487 
629 

770 

911 

*052 


929 
073 
216 

359 
501 
643 

785 

926 

*066 


943 

087 
230 

373 

515 
657 

799 

940 

*080 


958 
101 
244 

387 
530 
671 

813 

954 

*094 


972 
116 
259 

401 
544 
686 

827 

968 

*108 


986 
130 
273 

416 
558 
700 

841 

982 

*122 


310 


49 136 


150 


164 


178 


192 


206 


220 


234 


248 


262 


311 
312 
313 

314 
315 
316 

317 

318 
319 


276 
415 
554 

693 
831 
969 

50106 
243 
379 


290 
429 
568 

707 
845 
982 

120 
256 
393 


304 
443 

582 

721 
859 
996 

133 
270 
406 


318 
457 
596 

734 

872 
*010 

147 

284 
420 


332 
471 
610 

748 

886 

*024 

161 
297 
433 


346 

485 
624 

762 

900 

*037 

174 
311 

447 


360 
499 
638 

776 

914 

*051 

188 
325 
461 


374 
513 
651 

790 

927 

*065 

202 
338 
474 


388 
527 
665 

803 

941 

*079 

215 
352 

488 


402 
541 
679 

817 

955 

*092 

229 
365 
501 


1 
2 
3 
4 
5 
6 
7 
8 
9 


15 

1.5 

3.0 

4.5 

6.0 

7.5 

9.0 

10.5 

12.0 

1 3.5 


14 

1.4 

2.8 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 


320 


515 


529 


542 


556 


569 


583 


596 


610 


623 


637 




321 
322 
323 

324 
325 
326 

327 
328 
329 


651 
786 
920 

51055 

188 
322 

455 

587 
720 


664 
799 
934 

068 
202 
335 

468 
601 
733 


678 
813 
947 

081 
215 
348 

481 
614 

746 


691 
826 
961 

095 

228 
362 

495 
627 
759 


705 
840 
974 

108 
242 
375 

508 
640 

772 


718 
853 
987 

121 
255 

388 

521 
654 

786 


732 

866 

*001 

135 

268 
402 

534 
667 
799 


745 

880 

*014 

148 
282 
415 

548 
680 
812 


759 

893 

*028 

162 
295 

428 

561 
693 
825 


772 

907 

*041 

175 

308 
441 

574 
706 

838 




330 

331 
332 
333 

334 
335 
336 

337 

338 
339 

340 

341 
342 
343 

344 
345 
346 

347 
348 
349 


851 


865 


878 


891 


904 


917 


930 


'943 


957 


970 


983 

52 114 
244 

375 

504 
634 

763 
892 

53 020 


996 
127 
257 

388 
517 
647 

776 
905 
033 


*009 
140 
270 

401 
530 
660 

789 
917 
046 


*022 
153 

284 

414 
543 
673 

802 
930 
058 


*035 
166 
297 

427 
556 
686 

815 
943 
071 


*048 
179 
310 

440 
569 
699 

827 
956 
084 


*061 
192 
323 

453 

582 
711 

840 
969 

097 


*075 
205 
336 

466 
595 
724 

853 

982 
110 


*088 
218 
349 

479 
608 
737 

866 
994 
122 


♦101 
231 
362 

492 
621 
750 

879 

*007 

135 


1 
2 
3 
4 
5 
6 
7 
8 
9 


13 

1.3 
2.6 
3.9 
5.2 
6.5 
7.8 
9.1 
10.4 
11.7 


12 

1.2 

2.4 
3.6 

4.8 
6.0 
7.2 
8.4 
9.6 
10.8 


148 


161 


173 


186 


199 


212 


224 


237 


250 


263 


275 
403 
529 

656 

782 
908 

54 033 
158 
283 


288 
415 
542 

668 
794 
920 

045 
170 
295 


301 
428 
555 

681 
807 
933 

058 
183 
307 


314 
441 
567 

694 
820 
945 

070 
195 
320 


326 
453 
580 

706 
832 
958 

083 
208 
332 


339 
466 
593 

719 

845 
970 

095 
220 
345 


352 
479 
605 

732 

857 
983 

108 
233 
357 


364 
491 
618 

744 
870 
995 

120 
245 
370 


377 
504 
631 

757 

882 

*008 

133 

258 
382 


390 
517 
643 

769 

895 

*020 

145 
270 
394 




350 


407 


419 


432 


444 


456 


469 


481 


494 


506 


518 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




350 — 


Logarithms of Numbers — 


400 






7 


N. 
350 

351 
352 
353 

354 
355 
356 

357 
358 
359 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


54 407 


419 


432 


444 


456 


469 


481 


494 


506 


518 




531 
654 

777 

900 

55 023 

145 

267 

388 
509 


543 
667 
790 

913 
035 
157 

279 
400 
522 


555 
679 
802 

925 
047 
169 

291 
413 
534 


568 
691 
814 

937 
060 

182 

303 

425 
546 


580 
704 
827 

949 
072 
194 

315 
437 
558 


593 
716 
839 

962 

084 
206 

328 
449 
570 


605 
728 
851 

974 

096 
218 

340 
461 

582 


617 

741 
864 

986 
108 
230 

352 

473 
594 


630 
753 

876 

998 
121 
242 

364 

485 
606 


642 
765 

888 

*011 
133 
255 

376 

497 
618 


360 


630 


642 


654 


666 


678 


691 


703 


715 


727 


739 


361 
362 
363 

364 
365 
366 

367 
368 
369 


751 
871 
991 

56 110 
229 
348. 

467 
585 
703 


763 

883 
*003 

122 

241 
360 

478 
597 
714 


775 

895 

*015 

134 
253 
372 

490 
608 

726 


787 

907 

*027 

146 
265 
384 

502 
620 

738 


799 

919 

*038 

158 

277 
396 

514 
632 
750 


811 

931 

*050 

170 

289 
407 

526 
644 
761 


823 

943 

*062 

182 
301 
419 

538 
656 
773 


835 

955 

*074 

194 
312 
431 

549 

667 

785 


847 

967 

*086 

205 
324 
443 

561 
679 

797 


859 

979 

*098 

217 
336 
455 

573 
691 

808 


1 
2 
3 

4 
5 
6 
7 
8 
9 


13 

1.3 

2.6 
3.9 
5.2 
6.5 
7.8 
9.1 
10.4 
11.7 


12 

1.2 

2.4 
3.6 
4.8 
6.0 
7.2 
8.4 
9.6 
10.8 


370 


820 


832 


844 


855 


867 


879 


891 


902 


914 


926 




371 
372 
373 

374 
375 
376 

377 
378 
379 

380 


937 

57054 

171 

287 
403 
519 

634 

749 
864 


949 
066 
183 

299 
415 
530 

646 
761 

875 


961 
078 
194 

310 

426 
542 

657 

772 
887 


972 
089 
206 

322 
438 
553 

669 

784 
898 


984 
101 
217 

334 
449 
565 

680 
795 
910 


996 
113 
229 

345 
461 
576 

692 
807 
921 


*008 
124 
241 

357 
473 

588 

703 
818 
933 


*019 
136 
252 

368 

484 
600 

715 

830 
944 


*031 

148 
264 

380 
496 
611 

726 
841 
955 


*043 
159 
276 

392 

507 
623 

738 
852 
967 


978 


990 


*001 


*013 


*024 


*035 


*047 


*058 


*070 


*081 


381 
382 
383 

384 
385 
386 

387 

388 
389 


58 092 
206 
320 

433 
546 
659 

771 

883 
995 


104 
218 
331 

444 
557 
670 

782 

894 

*006 


115 
229 
343 

456 
569 
681 

794 

906 

*017 


127 
240 
354 

467 
580 
692 

805 
917 

*028 


138 
252 
365 

478 
591 
704 

816 

928 
*040 


149 
263 
377 

490 
602 
715 

827 

939 

*051 


161 

274 

388 

501 
614 
726 

838 

950 

*062 


172 
286 
399 

512 
625 
737 

850 
961 

*073 


184 
297 
410 

524 
636 
749 

861 
973 

*084 


195 

309 

422 

535 

647 
760 

872 

984 

*095 


1 
2 
3 
4 
5 
6 
7 
8 
9 


11 

1.1 

2.2 
3.3 
4.4 
5.5 
6.6 
7.7 
8.8 
9.9 


10 

1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 


390 


59 106 


118 


129 


140 


151 


162 


173 


184 


195 


207 




391 
392 
393 

394 
395 
396 

397 
398 
399 


218 
329 
439 

550 
660 
770 

879 

988 

60 097 


229 
340 
450 

561 
671 

780 

890 
999 
108 


240 
351 
461 

572 

682 
791 

901 

*010 

119 


251 
362 

472 

583 
693 
802 

912 

*021 

130 


262 
373 
483 

594 

704 
813 

923 

*032 

141 


273 

384 
494 

605 
715 
824 

934 

*043 

152 


284 
395 
506 

616 

726 
835 

945 

*054 
163 


295 
406 
517 

627 
737 
846 

956 

*065 

173 


306 
417 
528 

638 

748 
857 

966 

*076 

184 


318 

428 
539 

649 

759 

868 

977 

*086 

195 


400 


206 


217 


228 


239 


249 


260 


271 


282 


293 


304 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



8 




400 — 


Logarithms of Numbers — 


•450 






[I 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


400 


60 206 


217 


228 


239 


249 


260 


271 


282 


293 


304 




401 
402 
403 

404 
405 
406 

407 
408 
409 


314 
423 
531 

638 
746 
853 

959 

61066 

172 


325 
433 
541 

649 
756 
863 

970 
077 
183 


336 
444 
552 

660 
767 

874 

981 

087 
194 


347 
455 
563 

670 

778 
885 

991 
098 
204 


358 
466 
574 

681 

788 
895 

*002 
109 
215 


369 

477 
584 

692 
799 
906 

*013 
119 
225 


379 

487 
595 

703 
810 
917 

*023 
130 
236 


390 
498 
606 

713 

821" 
927 

*034 
140 

247 


401 
509 
617 

724 
831 
938 

*045 
151 

257 


412 
520 
627 

735 

842 
949 

*055 
162 

268 




10 

1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 


410 


278 


289 


300 


310 


321 


331 


342 


352 


363 


374 


1 
2 
3 
4 
5 
6 
7 
8 
9 


±JL 

1.1 

2.2 
3.3 

4.4 
5.5 

6.6 

7.7 
8.8 
9.9 


411 
412 
413 

414 
415 
416 

417 
418 
419 


384 
490 
595 

700 
805 
909 

62 014 
118 
221 


395 
500 
606 

711 

815 
920 

024 
128 
232 


405 
511 
616 

721 
826 
930 

034 
138 
242 


416 
521 
627 

731 

836 
941 

045 
149 
252 


426 
532 
637 

742 
847 
951 

055 
159 

263 


437 
542 
648 

752 

857 
962 

066 
170 
273 


448 
553 
658 

763 
868 
972 

076 
180 

284 


458 
563 
669 

773 

878 
982 

086 
190 
294 


469 
574 
679 

784 
888 
993 

097 
201 
304 


479 
584 
690 

794 

899 

*003 

107 
211 
315 


420 


325 


335 


346 


356 


366 


377 


387 


397 


408 


418 


logM 
=log [loge] 
=9.63778 431 

-10 


421 
422 
423 

424 
425 
426 

427 
428 
429 


428 
531 
634 

737 
839 
941 

63 043 

144 
246 


439 
542 
644 

747 
849 
951 

053 
155 
256 


449 
552 
655 

757 
859 
961 

063 
165 
266 


459 
562 
665 

767 
870 
972 

073 
175 

276 


469 
572 
675 

778 
880 
982 

083 

185 
286 


480 

583 
685 

788 
890 
992 

094 
195 
296 


490 
593 
696 

798 

900 

*002 

104 
205 
306 


500 
603 
706 

808 

910 

*012 

114 
215 
317 


511 
613 
716 

818 

921 

*022 

124 
225 
327 


521 
624 
726 

829 

931 

*033 

134 

236 
337 


430 


347 


357 


367 


377 


387 


397 


407 


417 


428 


438 

538 
639 
739 

839 

939 

*038 

137 
237 
335 


431 
432 
433 

434 
435 
436 

437 

438 
439 


448 
548 
649 

749 
849 
949 

64 048 
147 
246 


458 
558 
659 

759 
859 
959 

058 
157 
256 


468 
568 
669 

769 
869 
969 

068 
167 
266 


478 
579 
679 

779 
879 
979 

078 
177 
276 


488 
589 
689 

789 
889 
988 

088 
187 
286 


498 
599 
699 

799 
899 
998 

098 
197 
296 


508 
609 
709 

809 

909 

*008 

108 
207 
306 


518 
619 
719 

819 

919 

*018 

118 
217 
316 


528 
629 
729 

829 

929 

*028 

128 
227 
326 


1 
2 
3 
4 
5 
6 
7 
8 
9 


9 

0.9 
1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 


440 

441 
442 
443 

444 
445 
446 

447 
448 
449 


345 


355 


365 


375 


385 


395 


404 


414 


424 


434 


444 
542 
640 

738 
836 
933 

65 031 
128 
225 


454 
552 
650 

748 
846 
943 

040 
137 
234 


464 
562 
660 

758 
856 
953 

050 
147 
244 


473 
572 
670 

768 
865 
963 

060 
157 
254 


483 
582 
680 

777 
875 
972 

070 
167 
263 


493 
591 
689 

787 
885 
982 

079 
176 
273 


503 
601 
699 

797 
895^ 
992 

0£9 
186 

283 


513 
611 

709 

807 

904 

*002 

099 
196 

292 


523 
621 
719 

816 

914 

*011 

108 
205 
302 


532 
631 
729 

826 

924 

*021 

118 
215 
312 


450 


321 


331 


341 


350 


360 


369 


379 


389 


398 


408 




N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 



450 — Logarithms of Numbers — 500 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


450 


65 321 


331 


341 


350 


360 


369 


379 


389 


398 


408 




451 
452 
453 

454 
455 
456 

457 
458 
459 

460 


418 
514 
610 

706 
801 
896 

992 

66 087 

181 


427 
523 
619 

715 
811 
906 

*001 
096 
191 


437 
533 
629 

725 

820 
916 

*011 

106 
200 


447 
543 
639 

734 
830 
925 

*020 
115 
210 


456 
552 
648 

744 
839 
935 

*030 
124 
219 


466 
562 
658 

753 

849 
944 

*039 
134 
229 


475 
571 
667 

763 

858 
954 

*049 
143 

238 


485 
581 
677 

772 
868 
963 

*058 
153 

247 


495 
591 
686 

782 
877 
973 

*068 
162 

257 


504 
600 
696 

792 

887 
982 

*077 
172 
266 


276 


285 


295 


304 


314 


323 


332 


342 


351 


361 


461 
462 
463 

464 
465 
466 

467 
468 
469 


370 
464 

558 

652 

745 
839 

932 

67'025 

117 


380 
474 
567 

661 
755 

848 

941 
034 
127 


389 

483 

577 

671 

764 

857 

950 
043 
136 


398 
492 
586 

680 
773 

867 

960 
052 
145 


408 
502 
596 

689 

783 
876 

969 
062 
154 


417 
511 
605 

699 

792 
885 

978 
071 
164 


427 
521 
614 

708 
801 
894 

987 
080 
173 


436 
530 
624 

717 
811 
904 

997 
089 

182 


445 
539 
633 

727 
820 
913 

*006 
099 
191 


455 
549 
642 

736 

829 
922 

*015 
108 
201 


1 
2 
3 
4 
5 
6 
7 
8 
9 


10 

1.0 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 


9 

0.9 
1.8 

2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 


470 


210 


219 


228 


237 


247 


256 


265 


274 


284 


293 




471 

472 
473 

474 
475 
476 

477 
478 
479 


302 
394 

486 

578 
669 
761 

852 

943 

68 034 


311 
403 
495 

587 
679 
770 

861, 

952 

043 


321 
413 
504 

596 

688 
779 

870 
961 
052 


330 
422 
514 

605 
697 

788 

879 
970 
061 


339 
431 
523 

614 
706 
797 

888 
979 
070 


348 
440 
532 

624 
715 

806 

897 
988 
079 


357 
449 
541 

633 

724 
815 

906 

997 
088 


367 
459 
550 

642 
733 

825 

916 

*006 

097 


376 
468 
560 

651 

742 
834 

925 

*015 

106 


385 
477 
569 

660 
752 
843 

934 

*024 

115 


480 


124 


133 


142 


151 


160 


169 


178 


187 


196 


205 


481 

482 
483 

484 
485 
486 

487 
488 
489 


215 
305 
395 

485 
574 
664 

753 

842 
931 


224 
314 
404 

494 
583 
673 

762 
851 
940 


233 
323 
413 

502 
592 
681 

771 

860 
949 


242 
332 
422 

511 

601 
690 

780 
869 
958 


251 
341 
431 

520 

610 
699 

789 

878 
966 


260 
350 
440 

529 
619 

708 

797 
886 
975 


269 
359 
449 

538 

628 
717 

806 
895 
984 


278 
368 
458 

547 
637 
726 

815 
904 
993 


287 
377 
467 

556 
646 
735 

824 
913 

*002 


296 
386 

476 

565 
655 
744 

833 

922 

*011 


1 
2 
3 

4 
5 
6 
7 
8 
9 


8 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 


490 


69 020 


028 


037 


046 


055 


064 


073 


082 


090 


099 




491 
492 
493 

494 
495 
496 

497 

498 
499 


108 
197 
285 

373 

461 

548 

636 
723 
810 


117 

205 
294 

381 
469 
557 

644 
732 
819 


126 
214 
302 

390 

478 
566 

653 

740 

827 


135 
223 
311 

399 

487 
574 

662 
749 
836 


144 
232 
320 

408 
496 
583 

671 

758 
845 


152 
241 
329 

417 
504 
592 

679 
767 
854 


161 

249 
338 

425 
513 
601 

688 

775 
862 


170 

258 
346 

434 
522 
609 

697 

784 
871 


179 
267 
355 

443 
531 
618 

705 

793 

880 


188 
276 
364 

452 
539 
627 

714 
801 

888 


500 


897 


906 


914 


923 


932 


940 


949 


958 


966 


975 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop, Pts* 



10 




500 — 


Logarithms of Numbers — 


■550 








u. 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


500 


69 897 


906 


914 


923 


932 


940 


949 


958 


966 


975 


log 5 
=.69897 00043 


501 
502 
503 

504 
505 
506 

507 
508 
509 

510 


984 
70 070 

157 

243 
329 
415 

501 
586 
672 


992 
079 
165 

252 
338 
424 

509 
595 
680 


*001 

088 
174 

260 
346 
432 

518 
603 
689 


*010 
096 

183 

269 
355 
441 

526 
612 

697 


*018 
105 
191 

278 
364 
449 

535 

621 
706 


*027 
114 
200 

286 
372 

458 

544 
629 
714 


*036 
122 

209 

295 
381 
467 

552 

638 
723 


*044 
131 
217 

303 
389 
475 

561 
646 
731 


*053 
140 
226 

312 

398 

484 

569 
655 
740 


*062 
148 
234 

321 
406 
492 

578 
663 
749 


757 


766 


774 


783 


791 


800 


808 


817 


825 


834 


511 
512 
513 

514 
515 
516 

517 

518 
519 


842 

927 

71012 

096 
181 
265 

349 
433 
517 


851 
935 
020 

105 
189 
273 

357 
441 
525 


859 
944 
029 

113 

198 

282 

366 
450 
533 


868 
952 
037 

122 

206 
290 

374 

458 
542 


876 
961 
046 

130 

214 
299 

383 

466 
550 


885 
969 
054 

139 
223 
307 

391 
475 
559 


893 
978 
063 

147 
231 
315 

399 t 

483 
567 


902 
986 
071 

155 

240 
324 

408 
492 
575 


910 
995 
079 

164 

248 
332 

416 
500 
584 


919 

*003 

088 

172 
257 
341 

425 
508 
592 


1 
2 
3 
4 
5 
6 
7 
8 
9 


9 

0.9 
1.8 

2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 


8 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 


520 


600 


609 


617 


625 


634 


642 


650 


659 


667 


675 




521 
522 
523 

524 
525 
526 

527 

528 
529 

530 


684 
767 
850 

933 

72 016 

099 

181 
263 
346 


692 

775 
858 

941 
024 
107 

189 
272 
354 


700 
784 
867 

950 
032 
115 

198 
280 
362 


709 
792 

875 

958 
041 
123 

206 

288 
370 


717 
800 
883 

966 
049 
132 

214 
296 
378 


725 
809 
892 

975 
057 
140 

222 
304 
387 


734 
817 
900 

983 
066 

148 

230 
313 
395 


742 

825' 

908 

991 
074 
156 

239 
321 
403 


750 
834 
917 

999 
082 
165 

247 
329 
411 


759 
842 
925 

*008 
090 
173 

255 
337 
419 


428 


436 


444 


452 


460 


469 


477 


485 


493 


501 


531 
532 
533 

534 
535 
536 

537 
538 
539 


509 
591 
673 

754 
835 
916 

997 

73 078 

159 


518 
599 
681 

762 
843 
925 

*006 
086 
167 


526 
607 
689 

770 
852 
933 

*014 
094 
175 


534 
616 
697 

779 
860 
941 

*022 
102 
183 


542 
624 
705 

787 
868 
949 

*030 
111 
191 


550 
632 
713 

795 
876 
957 

*038 
119 
199 


558 
640 

722 

803 

884 
965 

*046 
127 
207 


567 
648 
730 

811 
892 
973 

*054 
135 
215 


575 
656 

738 

819 
900 
981 

*062 
143 
223 


583 
665 
746 

827 
908 
989 

*070 
151 
231 


1 
2 
3 
4 
5 
6 
7 
8 
9 


7 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 


540 


239 


247 


255 


263 


272 


280 


288 


296 


304 


312 




541 
542 
543 

544 
545 
546 

547 

548 
549 


320 
400 
480 

560 
640 
719 

799 
878 
957 


328 
408 

488 

568 
648 
727 

807 
886 
965 


336 
416 
496 

576 
656 
735 

815 
894 
973 


344 
424 
504 

584 
664 
743 

823 
902 
981 


352 
432 
512 

592 
672 
751 

830 
910 

989 


360 
440 
520 

600 
679 
759 

838 
918 
997 


368 
448 
528 

608 
687 
767 

846 

926 

*005 


376 
456 
536 

616 
695 

775 

854 

933 

*013 


384 
464 
544 

624 
703 

783 

862 

941 

*020 


392 
472 
552 

632 
711 
791 

870 

949 

*028 


550 


74 036 


044 


052 


060 


068 


076 


084 


092 


099 


107 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




550 — 


Logarith 


ms of Numbers — 


■600 






11 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


550 

551 
552 
553 


74 036 


044 


052 


060 


068 


076 


084 


092 


099 


107 




115 

194 
273 


123 

202 
280 


131 
210 

288 


139 
218 
296 


147 
225 
304 


155 
233 
312 


162 
241 
320 


170 
249 
327 


178 
257 
335 


186 
265 
343 


554 
555 
556 


351 

429 
507 


359 
437 
515 


367 
445 
523 


374 
453 
531 


382 

461 
539 


390 
468 
547 


398 
476 
554 


406 
484 
562 


414 
492 
570 


421 
500 

578 




557 
558 
559 


586 
663 

741 


593 
671 

749 


601 
679 

757 


609 

687 
764 


617 
695 

772 


624 
702 
780 


632 
710 

788 


640 

718 
796 


648 
726 
803 


656 
733 
811 




560 


819 


827 


834 


842 


850 


858 


865 


873 


881 


889 


561 
562 
563 


896 

974 

75 051 


904 
981 
059 


912 
989 
066 


920 
997 
074 


927 

*005 

082 


935 

*012 

089 


943 

*020 

097 


950 

*028 

105 


958 

*035 

113 


966 

*043 

120 


564 
565 
566 


128 
205 

282 


136 
213 
289 


143 

220 

297 


151 

228 
305 


159 
236 
312 


166 
243 
320 


174 
251 
328 


182 
259 
335 


189 
266 
343 


197 
274 
351 




567 
568 
569 

570 


358 
435 
511 


366 

442 
519 


374 
450 
526 


381 

458 
534 


389 
465 
542 


397 
473 
549 


404 
481 
557 


412 
488 
565 


420 
496 
572 


427 
504 
580 




587 


595 


603 


610 


618 


626 


633 


641 


648 


656 


571 
572 
573 


664 
740 
815 


671 

747 
823 


679 
755 
831 


686 
762 
838 


694 
770 
846 


702 
778 
853 


709 
785 
861 


717 
793 

868 


724 
800 
876 


732 
808 

884 


1 
2 


0.8 
1.6 


7 

0.7 
1.4 


574 
575 
576 

577 

578 
579 


891 

967 

76 042 

118 
193 

268 


899 
974 
050 

125 
200 
275 


906 
982 
057 

133 
208 
283 


914 
989 
065 

140 
215 
290 


921 

997 
072 

148 
223 
298 


929 

*005 

080 

155 

230 
305 


937 
*012 

087 

163 
238 
313 


944 

*020 

095 

170 
245 
320 


952 

*027 

103 

178 
253 

328 


959 

*035 

110 

185 
260 
335 


3 

4 
5 
6 
7 
8 
9 


2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 


2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 


580 


343 


350 


358 


365 


373 


380 


388 


395 


403 


410 




581 
582 
583 


418 
492 
567 


425 
500 
574 


433 
507 

582 


440 
515 
589 


448 
522 
597 


455 
530 
604 


462 
537 
612 


470 
545 
619 


477 
552 
626 


485 
559 
634 


584 
585 
586 


641 
716 
790 


649 
723 

797 


656 
730 
805 


664 
738 
812 


671 
745 
819 


678 
753 

827 


686 
760 
834 


693 

768 
842 


701 

775 
849 


708 
782 
856 




587 
588 
589 


864 

938 

77 012 


871 
945 
019 


879 
953 
026 


886 
960 
034 


893 
967 
041 


901 
975 
048 


908 
982 
056 


916 
989 
063 


923 
997 
070 


930 

*004 
078 




590 


085 


093 


100 


107 


115 


122 


129 


137 


144 


151 


591 
592 
593 


159 
232 
305 


166 
240 
313 


173 

247 
320 


181 
254 
327 


188 
262 
335 


195 
269 
342 


203 
276 
349 


210 

283 
357 


217 
291 
364 


225 
298 
371 


594 
595 
596 


379 
452 
525 


386 
459 
532 


393 
466 
539 


401 
474 
546 


408 
481 
554 


415 

488 
561 


422 
495 
568 


430 
503 
576 


437 
510 
583 


444 
517 
590 




597 
598 
599 


597 
670 
743 


605 
677 
750 


612 

685 

757 


619 
692 
764 


627 
699 

772 


634 
706 
779 


641 

714 

786 


648 
721 
793 


656 

728 
801 


663 

735 
808 




600 


815 


822 


830 


837 


844 


851 


859 


866 


873 


880 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



12 




600 — 


Logarithms of Numbers — 


650 








CI 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


600 


77 815 


822 


830 


837 


844 


851 


859 


866 


873 


880 




601 


887 


895 


902 


909 


916 


924 


931 


938 


945 


952 


602 


960 


967 


974 


981 


988 


996 


*003 


*010 


*017 


*025 




603 


78 032 


039 


046 


053 


061 


068 


075 


082 


089 


097 




604 


104 


111 


118 


125 


132 


140 


147 


154 


161 


168 




605 


176 


183 


190 


197 


204 


211 


219 


226 


233 


240 




606 


247 


254 


262 


269 


276 


283 


290 


297 


305 


312 




607 


319 


326 


333 


340 


347 


355 


362 


369 


376 


383 




608 


390 


398 


405 


412 


419 


426 


433 


440 


447 


455 




609 
610 


462 


469 


476 


483 


490 


497 


504 


512 


519 


526 




533 


540 


547 


554 


561 


569 


576 


583 


590 


597 


611 


604 


611 


618 


625 


633 


640 


647 


654 


661 


668 




B 


1 


612 


675 


682 


689 


696 


704 


711 


718 


725 


732 


739 


1 


0.8 


0.7 


613 


746 


753 


760 


767 


774 


781 


789 


796 


803 


810 


2 


1.6 


1.4 


614 


817 


824 


831 


838 


845 


852 


859 


866 


873 


880 


3 
4 
5 
6 


2.4 
3.2 

4.0 

4.8 


2.1 

2.8 
3.5 
4.2 


615 


888 


895 


902 


909 


916 


923 


930 


937 


944 


951 


616 


958 


965 


972 


979 


986 


993 


*000 


*007 


*014 


*021 


617 


79 029 


036 


043 


050 


057 


064 


071 


078 


085 


092 


7 


5.6 


4.9 


618 


099 


106 


113 


120 


127 


134 


141 


148 


155 


162 


8 


6.4 


5.6 


619 


169 


176 


183 


190 


197 


204 


211 


218 


225 


232 


9 


7.2 


6.3 


620 


239 


246 


253 


260 


267 


274 


281 


288 


295 


302 




621 


309 


316 


323 


330 


337 


344 


351 


358 


365 


372 


622 


379 


386 


393 


400 


407 


414 


421 


428 


435 


442 




623 


449 


456 


463 


470 


477 


484 


491 


498 


505 


511 




624 


518 


525 


532 


539 


546 


553 


560 


567 


574 


581 




625 


588 


595 


602 


609 


616 


623 


630 


637 


644 


650 




626 


657 


664 


671 


678 


685 


692 


699 


706 


713 


720 




627 


727 


734 


741 


748 


754 


761 


768 


775 


782 


789 




628 


796 


803 


810 


817 


824 


831 


837 


844 


851 


858 




629 


865 


872 


879 


886 


893 


900 


906 


913 


920 


927 




630 


934 


941 


948 


955 


962 


969 


975 


982 


989 


996 


631 


80 003 


010 


017 


024 


030 


037 


044 


051 


058 


065 




6 


632 


072 


079 


085 


092 


099 


106 


113 


120 


127 


134 


1 


0.6 


633 


140 


147 


154 


161 


168 


175 


182 


188 


195 


202 


2 


1.2 


634 


209 


216 


223 


229 


236 


243 


250 


257 


264 


271 


3 
4 
5 
6 


1.8 
2.4 
3.0 
3.6 


635 


277 


284 


291 


298 


305 


312 


318 


325 


332 


339 


636 


346 


353 


359 


366 


373 


380 


387 


393 


400 


407 


637 


414 


421 


428 


434 


441 


448 


455 


462 


468 


475 


7 


4.2 


638 


482 


489 


496 


502 


509 


516 


523 


530 


536 


543 


8 


4.8 


639 
640 

641 


550 


557 


564 


570 


577 


584 


591 


598 


604 


611 


9 


5.4 


618 


625 


632 


638 


645 


652 


659 


665 


672 


679 




686 


693 


699 


706 


713 


720 


726 


733 


740 


747 


642 


754 


760 


767 


774 


781 


787 


794 


801 


808 


814 




643 


821 


828 


835 


841 


848 


855 


862 


868 


875 


882 




644 


889 


895 


902 


909 


916 


922 


929 


936 


943 


949 




645 


956 


963 


969 


976 


983 


990 


996 


*003 


*010 


*017 




646 


81023 


030 


037 


043 


050 


057 


064 


070 


077 


084 




647 


090 


097 


104 


111 


117 


124 


131 


137 


144 


' 151 




648 


158 


164 


171 


178 


184 


191 


198 


204 


211 


218 




649 


224 


231 


238 


245 


251 


258 


265 


271 


278 


285 




650 


291 


298 


305 


311 


318 


325 


331 


338 


345 


351 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts, 



I] 




650 — 


Logarithm 


ms of Numbers — 


■700 






13 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


650 


81291 


298 


305 


311 


318 


325 


331 


338 


345 


351 




651 
652 
653 

654 
655 
656 

657 
658 
659 


358 
425 
491 

558 
624 
690 

757 
823 
889 


365 
431 

498 

564 
631 
697 

763 

829 
895 


371 
438 
505 

571 

637 
704 

770 
836 
902 


378 

445 
511 

578 
644 
710 

776 

842 
908 


385 
451 
518 

584 
651 
717 

783 
849 
915 


391 
458 
525 

591 
657 
723 

790 
856 
921 


398 
465 
531 

598 
664 
730 

796 
862 

928 


405 
471 
538 

604 
671 
737 

803 
869 
935 


411 

478 
544 

611 
677 
743 

809 
875 
941 


418 
485 
551 

617 
684 
750 

816 

882 
948 


660 


954 


961 


968 


974 


981 


987 


994 


*000 


*007 


*014 


661 
662 
663 

664 
665 
666 

667 
668 
669 


82 020 
086 
151 

217 
282 
347 

413 

478 
543 


027 
092 
158 

223 
289 
354 

419 
484 
549 


033 
099 
164 

230 
295 
360 

426 
491 
556 


040 
105 
171 

236 
302 
367 

432 
497 
562 


046 
112 

178 

243 
308 
373 

439 
504 
569 


053 
119 

184 

249 
315 
380 

445 
510 
575 


060 
125 
191 

256 
321 

387 

452 
517 

582 


066 
132 
197 

263 
328 
393 

458 
523 

588 


073 
138 
204 

269 
334 
400 

465 
530 
595 


079 
145 
210 

276 
341 

406 

471 
536 
601 


670 


607 


614 


620 


627 


633 


640 


646 


653 


659 


666 


671 
672 
673 

674 
675 
676 

677 
678 
679 

680 


672 
737 
802 

866 
930 
995 

83 059 
123 

187 


679 
743 

808 

872 

937 

*001 

065 
129 
193 


685 
750 
814 

879 

943 

*008 

072 
136 
200 


692 
756 
821 

885 

950 

*014 

078 
142 
206 


698 
763 

827 

892 

956 

*020 

085 
149 
213 


705 
769 
834 

898 

963 

*027 

091 
155 
219 


711 

776 
840 

905 

969 

*033 

097 
161 
225 


718 
782 
847 

911 

975 

*040 

104 
168 
232 


724 
789 
853 

918 

982 

*046 

110 
174 
238 


730 
795 
860 

924 

988 
*052 

117 
181 
245 


1 
2 
3 
4 
5 
6 
7 
8 
9 


7 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 


6 

0.6 
1.2 

1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 


251 


257 


264 


270 


276 


283 


289 


296 


302 


308 




681 
682 
683 

684 
685 
686 

687 
688 
689 


315 
378 
442 

506 
569 
632 

696 
759 
822 


321 
385 

448 

512 
575 
639 

702 
765 

828 


327 
391 
455 

518 

582 
645 

708 
771 
835 


334 
398 
461 

525 

588 
651 

715 
778 
841 


340 
404 
467 

531 
594 
658 

721 

784 
847 


347 
410 
474 

537 
601 
664 

727 
790 
853 


353 
417 
480 

544 
607 
670 

734 

797 
860 


359 
423 

487 

550 
613 
677 

740 
803 
866 


366 
429 
493 

556 
620 
683 

746 
809 

872 


372 
436 
499 

563 
626 
689 

753 

816 

879 


690 


885 


891 


897 


904 


910 


916 


923 


929 


935 


942 


691 
692 
693 

694 
695 
696 

697 
698 
699 


948 

84 011 

073 

136 

198 
261 

323 
386 

448 


954 
017 
080 

142 
205 
267 

330 
392 
454 


960 
023 
086 

148 
211 
273 

336 

398 
460 


967 
029 
092 

155 
217 
280 

342 

404 
466 


973 
036 
098 

161 
223 

286 

348 
410 
473 


979 
042 
105 

167 
230 
292 

354 

417 
479 


985 
048 
111 

173 
236 
298 

361 
423 

485 


992 
055 
117 

180 
242 
305 

367 
429 
491 


998 
061 
123 

186 
248 
311 

373 
435 
497 


*004 
067 
130 

192 
255 
317 

379 

442 
504 


700 


510 


516 


522 


528 


535 


541 


547 


553 


559 


566 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



14 




700 — 


Logarithms of Numbers — 


750 








d 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


700 


84 510 


516 


522 


528 


535 


541 


547 


553 


559 


566 


log 7 
= .84509 80400 


701 
702 
703 

704 
705 
706 

707 
708 
709 


572 
634 
696 

757 
819 
880 

942 

85 003 

065 


578 
640 
702 

763 
825 

887 

948 
009 
071 


584 
646 
708 

770 
831 
893 

954 
016 

077 


590 
652 
714 

776 
837 
899 

960 
022 
083 


597 
658 
720 

782 
844 
905 

967 
028 
089 


603 
665 
726 

788 
850 
911 

973 

034 
095 


609 
671 
733 

794 
856 
917 

979 
040 
101 


615 
677 
739 

800 
862 
924 

985 
046 
107 


621 
683 
745 

807 
868 
930 

991 
052 
114 


628 
689 
751 

813 

874 
936 

997 
058 
120 


710 


126 


132 


138 


144 


150 


156 


163 


169 


175 


181 


711 
712 
713 

714 
715 
716 

717 

718 
719 


187 
248 
309 

370 
431 
491 

552 
612 
673 


193 
254 
315 

376 

437 
497 

558 
618. 
679 


199 
260 
321 

382 
443 
503 

564 
625 

685 


205 
266 
327 

388 
449 
509 

570 
631 
691 


211 
272 
333 

394 
455 
516 

576 
637 
697 


217 
278 
339 

400 
461 
522 

582 
643 
703 


224 
285 
345 

406 
467 

528 

588 
649 
709 


230 
291 
352 

412 
473 
534 

594 
655 
715 


236 
297 
358 

418 
479 
540 

600 
661 
721 


242 
303 
364 

425 

485 
546 

606 
667 

727 


1 
2 
3 

4 
5 
6 
7 
8 
9 


4 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 


b 

0.6 
1.2 

1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 


720 


733 


739 


745 


751 


757 


763 


769 


775 


781 


788 




721 
722 
723 

724 
725 
726 

727 
728 
729 


794 
854 
914 

974 

86 034 

094 

153 
213 
273 


800 
860 
920 

980 
040 
100 

159 
219 
279 


806 
866 
926 

986 
046 
106 

165 
225 

285 


812 
872 
932 

992 
052 
112 

171 
231 
291 


818 
878 
938 

998 
058 
118 

177 
237 
297 


824 
884 
944 

*004 
064 
124 

183 
243 
303 


830 
890 
950 

*010 
070 
130 

189 
249 
308 


836 
896 
956 

*016 
076 
136 

195 
255 
314 


842 
902 
962 

*022 
082 
141 

201 
261 
320 


848 
908 
968 

*028 
088 
147 

207 
267 
326 


730 


332 


338 


344 


350 


356 


362 


368 


374 


380 


386 


1 
2 
3 
4 
5 
6 
7 
8 
9 


5 

0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


731 
732 
733 

734 
735 
736 

737 

738 
739 


392 
451 
510 

570 
629 

688 

747 
806 
864 


398 
457 
516 

576 
635 
694 

753 

812 
870 


404 
463 
522 

581 
641 
700 

759 
817 
876 


410 
469 

528 

587 
646 
705 

764 
823 

882 


415 
475 
534 

593 
652 
711 

770 

829 

888 


421 

481 
540 

599 
658 
717 

776 
835 
894 


427 
487 
546 

605 
664 
723 

782 
841 
900 


433 
493 
552 

611 
670 
729 

788 
847 
906 


439 
499 
558 

617 
676 
735 

794 
853 
911 


445 
504 
564 

623 

682 
741 

800 
859 
917 


740 


923 


929 


935 


941 


947 


953 


958 


964 


970 


976 




741 

742 
743 

744 
745 
746 

747 
748 
749 


982 

87 040 

099 

157 
216 
274 

332 
390 

448 


988 
046 
105 

163 
221 
280 

338 
396 
454 


994 
052 
111 

169 
227 
286 

344 

402 
460 


999 
058 
116 

175 
233 
291 

349 

408 
466 


*005 
064 
122 

181 
239 
297 

355 
413 
471 


*011 
070 
128 

186 
245 
303 

361 
419 

477 


*017 
075 
134 

192 
251 
309 

367 
425 
483 


*023 
081 
140 

198 
256 
315 

373 
431 

489 


*029 
087 
146 

204 
262 
320 

379 

437 
495 


*035 
093 
151 

210 
268 
326 

384 
442 
500 


750 


506 


512 


518 


523 


529 


535 


541 


547 


552 


558 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




750 — 


Logarithms of Numbers — 


800 






15 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


750 


87 506 


512 


518 


523 


529 


535 


541 


547 


552 


558 




751 
752 
753 

754 
755 
756 

757 
758 
759 


564 
622 
679 

737 
795 

852 

910 
967 

88 024 


570 
628 
685 

743 

800 

858 

915 
973 
030 


576 
633 
691 

749 
806 
864 

921 

978 
036 


581 
639 
697 

754 
812 
869 

927 
984 
041 


587 
645 
703 

760 

818 
875 

933 
990 
047 


593 
651 

708 

766 
823 

881 

938 
996 
053 


599 
656 
714 

772 
829 
887 

944 

*001 

058 


604 
662 
720 

777 
835 
892 

950 

*007 

064 


610 

668 
726 

783 
841 
898 

955 

*013 

070 


616 
674 
731 

789 
846 
904 

961 

*018 

076 


760 


081 


087 


093 


098 


104 


110 


116 


121 


127 


133 


761 
762 
763 

764 
765 
766 

767 

768 
769 


138 
195 
252 

309 
366 
423 

480 
536 
593 


144 
201 
258 

315 
372 

429 

485 
542 
598 


150 
207 
264 

321 
377 
434 

491 
547 
604 


156 
213 

270 

326 
383 
440 

497 
553 

610 


161 
218 
275 

332 

389 
446 

502 
559 
615 


167 
224 
281 

338 
395 
451 

508 
564 
621. 


173 
230 

287 

343 
400 
457 

513 
570 
627 


178 
235 
292 

349 
406 
463 

519 
576 
632 


184 
241 

298 

355 

412 

468 

525 

581 
638 


190 

247 
304 

360 
417 
474 

530 

587 
643 


770 


649 


655 


660 


666 


672 


677 


683 


689 


694 


700 


771 

772 
773 

774 
775 
776 

777 
778 
779 


705 
762 

818 

874 
930 
986 

89 042 
098 
154 


711 

767 

824 

880 
936 
992 

048 
104 
159 


717 
773 
829 

885 
941 
997 

053 
109 
165 


722 
779 
835 

891 

947 

*003 

059 
115 
170 


728 
784 
840 

897 

953 

*009 

064 
120 
176 


734 

790 
846 

902 

958 

*014 

070 
126 
182 


739 
795 

852 

908 

964 

*020 

076 
131 

187 


745 

801 

857 

913 

969 

*025 

081 
137 
193 


750 
807 
863 

919 

975 

*031 

087 
143 
198 


756 
812 

868 

925 

981 
*037 

092 
148 
204 


1 
2 
3 

4 
5 
6 

7 
8 
9 


6 

0.6 
1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 


5 

0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


780 


209 


215 


221 


226 


232 


237 


243 


248 


254 


260 




781 
782 
783 

784 
785 
786 

787 
788 
789 


265 
321 
376 

432 

487 
542 

597 
653 

708 


271 
326 
382 

437 

492 

Oio 

603 
658 
713 


276 
332 

387 

443 
498 
553 

609 
664 
719 


282 
337 
393 

448 
504 
559 

614 
669 
724 


287 
343 
398 

454 
509 
564 

620 
675 
730 


293 
348 
404 

459 
515 
570 

625 
680 
735 


298 
354 
409 

465 
520 
575 

631 
686 
741 


304 
360 
415 

470 
526 
581 

636 
691 
746 


310 
365 
421 

476 
531 
586 

642 
697 
752 


315 
371 
426 

481 
537 
592 

647 
702 

757 


790 


763 


768 


774 


779 


785 


790 


796 


801 


807 


812 


791 
792 
793 

794 
795 
796 

797 
798 
799 


818 
873 
927 

982 

90 037 

091 

146 
200 
255 


823 
878 
933 

988 
042 
097 

151 

206 
260 


829 
883 
938 

993 
048 
102 

157 
211 

266 


834 

889 
944 

998 
053 
108 

162 
217 
271 


840 
894 
949 

*004 
059 
113 

168 
222 
276 


845 
900 
955 

*009 
064 
119 

173 

227 
282 


851 
905 
960 

*015 
069 
124 

179 
233 

287 


856 
911 
966 

*020 
075 
129 

184 
238 
293 


862 
916 
971 

*026 
080 
135 

189 
244 

298 


867 
922 

977 

*031 

086 
140 

195 

249 
304 


800 


309 


314 


320 


325 


331 


336 


342 


347 


352 


358 


N. | 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



16 




800 — 


Logarith] 


tns of Numbers — 


-850 






CI 


N. 
800 

801 
802 
803 

804 
805 
806 

807 
808 
809 

810 





l 


2 


3 


4 


8 


6 


7 


8 


9 


Prop. Pts. 


90 309 


314 


320 


325 


331 


336 


342 


347 


352 


358 




363 
417 
472 

526 
580 
634 

687 
741 
795 


369 
423 

477 

531 

585 
639 

693 

747 
800 


374 

428 
482 

536 
590 
644 

698 
752 
806 


380 
434 

488 

542 
596 
650 

703 

757 
811 


385 

439 
493 

547 
601 
655 

709 
763 
816 


390 
445 
499 

553 

607 
660 

714 

768 
822 


396 
450 
504 

558 
612 
666 

720 
773 

827 


401 
455 
509 

563 
617 
671 

725 

779 
832 


407 
461 
515 

569 
623 
677 

730 

784 
838 


412 
466 
520 

574 

628 
682 

736 

789 
843 


849 


854 


859 


865 


870 


875 


881 


886 


891 


897 


811 
812 
813 

814 
815 
816 

817 
818 
819 

820 


902 

956 

91009 

062 
116 
169 

222 
275 
328 


907 
961 
014 

068 
121 
174 

228 
281 
334 


913 
966 
020 

073 
126 
180 

233 

286 
339 


918 
972 
025 

078 
132 
185 

238 
291 
344 


924 
977 
030 

084 
137 
190 

243 

297 
350 


929 

982 
036 

089 
142 
196 

249 
302 
355 


934 

988 
041 

094 
148 
201 

254 
307 
360 


940 
993 
046 

100 
153 

206 

259 
312 
365 


945 
998 
052 

105 
158 
212 

265 
318 
371 


950 

*004 

057 

110 
164 
217 

270 
323 
376 


381 


387 


392 


397 


403 


408 


413 


418 


424 


429 


821 
822 
823 

824 
825 
826 

827 
828 
829 


434 
487 
540 

593 
645 
698 

751 
803 
855 


440 
492 
545 

598 
651 
703 

756 
808 
861 


445 

498 
551 

603 
656 
709 

761 
814 
866 


450 
503 
556 

609 
661 
714 

766 
819 
871 


455 
508 
561 

614 
666 
719 

772 
824 
876 


461 
514 
566 

619 
672 

724 

777 
829 
882 


466 
519 
572 

624 
677 
730 

782 
834 

887 


471 
524 
577 

630 

682 
735 

787 
840 
892 


477 
529 

582 

635 

687 
740 

793 

845 
897 


482 
535 

587 

640 
693 
745 

798 
850 
903 


1 
2 
3 
4 
5 
6 
7 
8 
9 


b 

0.6 
1.2 

1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 


5 

0.5 
1.0 

1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


830 


908 


913 


918 


924 


929 


934 


939 


944 


950 


955 




831 
832 
833 

834 
835 
836 

837 
838 
839 

840 


960 

92 012 

065 

117 

169 
221 

273 
324 
376 


965 
018 
070 

122 

174 
226 

278 
330 
381 


971 
023 
075 

127 
179 
231 

283 
335 

387 


976 
028 
080 

132 

184 
236 

288 
340 
392 


981 
033 
085 

137 
189 
241 

293 
345 
397 


986 
038 
091 

143 

195 

247 

298 
350 
402 


991 
044 
096 

148 
200 
252 

304 
355 

407 


997 
049 
101 

153 

205 
257 

309 
361 
412 


*002 
054 
106 

158 
210 
262 

314 

366 
418 


*007 
059 
111 

163 
215 

267 

319 
371 
423 


428 


433 


438 


443 


449 


454 


459 


464 


469 


474 


841 
842 
843 

844 
845 
846 

847 
848 
849 


480 
531 
583 

634 
686 
737 

788 
840 
891 


485 
536 

588 

639 

691 

742 

793 

845 
896 


490 
542 
593 

645 
696 

747 

799 
850 
901 


495 

547 
598 

650 
701 
752 

804 
855 
906 


500 
552 
603 

655 

706 

758 

809 
860 
911 


505 
557 
609 

660 
711 
763 

814 
865 
916 


511 
562 
614 

665 
716 

768 

819 
870 
921 


516 
567 
619 

670 

722 
773 

824 
875 
927 


521 

572 
624 

675 

727 
778 

829 
881 
932 


526 
578 
629 

681 
732 

783 

834 
886 
937 


850 


942 


947 


952 


957 


962 


967 


973 


978 


983 


988 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




850 — 


Logarithms of Numbers — 


■900 








17 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


850 


92 942 


947 


952 


957 


962 


967 


973 


978 


983 


988 




851 
852 
853 


993 

93 044 

095 


998 
049 
100 


*003 
054 
105 


*008 
059 
110 


*013 
064 
115 


*018 
069 
120 


*024 
075 
125 


*029 
080 
131 


*034 
085 
136 


*039 
090 
141 


854 
855 
856 


146 
197 
247 


151 
202 
252 


156 
207 

258 


161 
212 
263 


166 
217 

268 


171 
222 
273 


176 

227 
278 


181 
232 
283 


186 
237 

288 


192 
242 
293 




857 
858 
859 


298 
349 
399 


303 
354 
404 


308 
359 
409 


313 
364 
414 


318 
369 
420 


323 
374 
425 


328 
379 
430 


334 

384 
435 


339 
389 
440 


344 
394 
445 




860 


450 


455 


460 


465 


470 


475 


480 


485 


490 


495 


861 
862 
863 


500 
551 
601 


505 
556 
606 


510 
561 
611 


515 

566 
616 


520 
571 
621 


526 
576 
626 


531 
581 
631 


536 
586 
636 


541 
591 
641 


546 
596 
646 


1 

2 


0.6 
1.2 


O 

0.5 
1.0 


864 
865 
866 

867 
868 
869 

870 


651 
702 
752 

802 
852 
902 


656 

707 

757 

807 
857 
907 


661 
712 
762 

812 
862 
912 


666 
717 
767 

817 
867 
917 


671 
722 

772 

822 
872 
922 


676 

727 
777 

827 
877 
927 


682 
732 

782 

832 
882 
932 


687 
737 

787 

837 
887 
937 


692 

742 
792 

842 
892 
942 


697 

747 
797 

847 
897 
947 


3 
4 
5 
6 

7 
8 
9 


1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 


1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


952 


957 


962 


967 


972 


977 


982 


987 


992 


997 




871 
872 
873 


94 00S 
05i 
101 


007 
057 
106 


012 
062 
111 


017 
067 
116 


022 
072 
121 


027 
077 
126 


032 
082 
131 


037 
086 
136 


042 
091 
141 


047 
096 
146 


874 
875 
876 


151 

201 
250 


156 
206 
255 


161 
211 
260 


166 
216 
265 


171 
221 
270 


176 
226 
275 


181 
231 

280 


186 
236 

285 


191 
240 
290 


196 
245 
295 




877 
878 
879 


300 
349 
399 


305 
354 

404 


310 
359 

409 


315 

364 
414 


320 
369 
419 


325 
374 
424 


330 
379 
429 


335 
384 
433 


340 
389 
438 


345 
394 
443 




880 


448 


453 


458 


463 


468 


473 


478 


483 


488 


493 


881 
882 
883 


498 
547 
596 


503 
552 
601 


507 
557 
606 


512 
562 
611 


517 
567 
616 


522 
571 
621 


527 
576 
626 


532 
581 
630 


537 

586 
635 


542 
591 
640 


1 
2 


4 

0.4 

0.8 


884 
885 
886 


645 

694 
743 


650 
699 

748 


655 
704 
753 


660 

709 

758 


665 
714 
763 


670 
719 

768 


675 
724 
773 


680 

729 

778 


685 
734 
783 


689 

738 
787 


3 
4 
5 
6 


1.2 
1.6 

2.0 
2.4 


887 
888 
889 


792 
841 
890 


797 

846 
895 


802 
851 
900 


807 
856 
905 


812 
861 
910 


817 
866 
915 


822 
871 
919 


827 
876 
924 


832 
880 
929 


836 
885 
934 


7 
8 
9 


2.8 
3.2 
3.6 


890 


939 


944 


949 


954 


959 


963 


968 


973 


978 


983 




891 
892 
893 


988 

95 036 

085 


993 
041 
090 


998 
046 
095 


*002 
051 
100 


*007 
056 
105 


*012 
061 
109 


*017 
066 
114 


*022 
071 
119 


*027 
075 
124 


*032 
080 
129 


894 
895 
896 


134 

182 
231 


139 

187 
236 


143 
192 
240 


148 
197 
245 


153 

202 
250 


158 
207 
255 


163 
211 
260 


168 
216 
265 


173 

221 
270 


177 
226 
274 




897 
898 
899 


279 
328 
376 


284 
332 
381 


289 
337 
386 


294 
342 
390 


299 
347 
395 


303 
352 

400 


308 
357 
405 


313 
361 
410 


318 
366 
415 


323 
371 

419 




900 


424 


429 


434 


439 


444 


448 


453 


458 


463 


468 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



18 




900 — 


Logarith 


tns of Numbers — 


-950 






[I 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. 


Pts. 


900 


95 424 


429 


434 


439 


444 


448 


453 


458 


463 


468 




901 
902 
903 


472 
521 
569 


477 
525 
574 


482 
530 

578 


487 
535 
583 


492 
540 

588 


497 
545 
593 


501 
550 

598 


506 
554 
602 


511 
559 
607 


516 
564 
612 


904 
905 
906 


617 
665 
713 


622 
670 

718 


626 
674 
722 


631 
679 

727 


636 
684 
732 


641 
689 
737 


646 
694 

742 


650 
698 
746 


655 
703 
751 


660 

708 
756 




907 
908 
909 


761 
809 
856 


766 
813 
861 


770 

818 
866 


775 
823 

871 


780 

828 
875 


785 
832 
880 


789 
837 

885 


794 
842 
890 


799 

847 
895 


804 
852 
899 




910 


904 


909 


914 


918 


923 


928 


933 


938 


942 


947 


911 
912 
913 


952 

999 

96 047 


957 

*004 

052 


961 

*009 

057 


966 

*014 

061 


971 

*019 

066 


976 

*023 

071 


980 

*028 

076 


985 

*033 

080 


990 

*038 

085 


995 

*042 

090 


914 
915 
916 


095 
142 
190 


099 
147 
194 


104 
152 
199 


109 
156 
204 


114 
161 
209 


118 
166 
213 


123 
171 

218 


128 
175 
223 


133 
180 
227 


137 
185 
232 




917 
918 
919 


237 

284 
332 


242 
289 
336 


246 
294 
341 


251 
298 
346 


256 
303 
350 


261 
308 
355 


265 
313 
360 


270 

317 
365 


275 
322 
369 


280 
327 
374 




920 


379 


384 


388 


393 


398 


402 


407 


412 


417 


421 


921 
922 
923 


426 
473 
520 


431 

478 
525 


435 

483 
530 


440 
487 
534 


445 
492 
539 


450 
497 
544 


454 
501 
548 


459 
506 
553 


464 
511 
558 


468 
515 
562 


1 
2 




0.5 
1.0 


4 

0.4 

0.8 


924 
925 
926 

927 
928 
929 


567 
614 
661 

708 
755 
802 


572 

619 
666 

713 
759 
806 


577 
624 
670 

717 

764 
811 


581 
628 
675 

722 

769 
816 


586 
633 
680 

727 
774 
820 


591 
638 
685 

731 

778 
825 


595 
642 
689 

736 
783 
830 


600 
647 
694 

741 

788 
834 


605 
652 
699 

745 
792 
839 


609 
656 
703 

750 

797 
844 


3 
4 
5 
6 

7 
8 
9 


1.5 

2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


1.2 

1.6 

2.0 

2.4 . 

2.8 

3.2 

3.6 


930 


848 


853 


858 


862 


867 


872 


876 


881 


886 


890 




931 
932 
933 


895 
942 

988 


900 
946 
993 


904 
951 
997 


909 

956 

*002 


914 

960 

*007 


918 

965 

*011 


923 

970 

*016 


928 

974 

*021 


932 

979 

*025 


937 

984 

*030 


934 
935 
936 


97 035 
081 
128 


039 
086 
132 


044 
090 
137 


049 
095 
142 


053 
100 
146 


058 
104 
151 


063 
109 
155 


067 
114 
160 


072 
118 
165 


077 
123 
169 




937 
938 
939 


174 

220 
267 


179 
225 
271 


183 
230 
276 


188 
234 
280 


192 
239 

285 


197 
243 
290 


202 

248 
294 


206 
253 
299 


211 
257 
304 


216 
262 
308 




940 


313 


317 


322 


327 


331 


336 


340 


345 


350 


354 


941 
942 
943 


359 
405 
451 


364 
410 
456 


368 
414 
460 


373 
419 
465 


377 
424 
470 


382 

428 
474 


387 
433 
479 


391 
437 

483 


396 
442 

488 


400 
447 
493 


944 
945 
946 


497 
543 

589 


502 
548 
594 


506 
552 
598 


511 
557 
603 


516 
562 
607 


520 
566 
612 


525 
571 
617 


529 
575 
621 


534 
580 
626 


539 
585 
630 




947 
948 
949 


635 
681 

727 


640 
685 
731 


644 
690 
736 


649 
695 

740 


653 

699 

745 


658 
704 

749 


663 

'708 
754 


667 
713 
759 


672 
717 
763 


676 

722 
768 




950 


772 


777 


782 


786 


791 


795 


800 


804 


809 


813 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



I] 




950 — Logarithms of Numbers — 


1000 




19 


N. 





l 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 


950 

951 
952 
953 


97 772 


777 


782 


786 


791 


795 


800 


804 


809 


813 




818 
864 
909 


823 
868 
914 


827 
873 
918 


832 

877 
923 


836 

882 
928 


841 
886 
932 


845 
891 
937 


850 
896 
941 


855 
900 
946 


859 
905 
950 


954 
955 
956 


955 

98 000 

046 


959 
005 
050 


964 
009 
055 


968 
014 
059 


973 
019 
064 


978 
023 
068 


982 
028 
073 


987 
032 
078 


991 
037 
082 


996 
041 
087 




957 
958 
959 


091 
137 
182 


096 
141 
186 


100 
146 
191 


105 
150 
195 


109 
155 

200 


114 
159 

204 


118 
164 
209 


123 

168 
214 


127 
173 

218 


132 
177 
223 




960 


227 


232 


236 


241 


245 


250* 


254 


259 


263 


268 


961 
962 
963 


272 
318 
363 


277 
322 
367 


281 
327 
372 


286 
331 
376 


290 
336 
381 


295 
340 
385 


299 
345 
390 


304 
349 
394 


308 
354 
399 


313 
358 
403 


964 
965 
966 


408 
453 
498 


412 
457 
502 


417 
462 
507 


421 
466 
511 


426 
471 
516 


430 
475 
520 


435 
480 
525 


439 

484 
529 


444 
489 
534 


448 
493 
538 




967 
968 
969 


543 

588 
632 


547 
592 
637 


552 
597 
641 


556 
601 
646 


561 
605 
650 


565 
610 
655 


570 
614 
659 


574 
619 
664 


579 
623 

668 


583 

628 
673 




970 

971 
972 
973 


677 


682 


686 


691 


695 


700 


704 


709 


713 


717 


722 
767 
811 


726 
771 

816 


731 

776 
820 


735 
780 
825 


740 

784 
829 


744 
789 
834 


749 
793 
838 


753 

798 
843 


758 
802 
847 


762 
807 
851 


1 
2 


d 

0.5 

1.0 


4 

0.4 

0.8 


974 
975 
976 

977 

978 
979 


856 
900 
945 

989 

99 034 

078 


860 
905 
949 

994 
038 
083 


865 
909 
954 

998 
043 
087 


869 
914 
958 

*003 
047 
092 


874 
918 
963 

*007 
052 
096 


878 
923 
967 

*012 
056 
100 


883 
927 
972 

*016 
061 
105 


887 
932 
976 

*021 
065 
109 


892 
936 
981 

*025 
069 
114 


896 
941 
985 

*029 
074 
118 


3 
4 
5 
6 
7 
8 
9 


1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 


1.2 
1.6 
2.0 
2.4 
2.8 
3.2 
3.6 


980 


123 


127 


131 


136 


140 


145 


149 


154 


158 


162 




981 
982 
983 


167 
211 
255 


171 
216 
260 


176 
220 
264 


180 
224 
269 


185 
229 
273 


189 
233 

277 


193 

238 

282 


198 
242 

286 


202 
247 
291 


207 
251 
295 


984 
985 
986 


300 
344 

388 


304 
348 
392 


308 
352 
396 


313 
357 
401 


317 
361 
405 


322 
366 
410 


326 
370 
414 


330 
374 
419 


335 
379 
423 


339 
383 
427 




987 
988 
989 


432 
476 
520 


436 
480 
524 


441 

484 
528 


445 
489 
533 


449 
493 
537 


454 
498 
542 


458 
502 
546 


463 
506 
550 


467 
511 
555 


471 
515 
559 




990 


564 


568 


572 


577 


581 


585 


590 


594 


599 


603 


991 
992 
993 


607 
651 
695 


612 
656 
699 


616 
660 
704 


621 
664 

708 


625 
669 
712 


629 
673 

717 


634 
677 
721 


638 
682 
726 


642 
686 
730 


647 
691 
734 


994 
995 
996 


739 

782 
826 


743 

787 
830 


747 
791 
835 


752 
795 
839 


756 
800 
843 


760 

804 

848 


765 
808 
852 


769 
813 
856 


774 
817 
861 


778 
822 
865 




997 
998 
999 


870 
913 
957 


874 
917 
961 


878 
922 
965 


883 
926 
970 


887 
930 
974 


891 
935 
978 


896 
939 
983 


900 
944 

987 


904 
948 
991 


909 
952 
996 




1000 


00 000 


004 


009 


013 


017 


022 


026 


030 


035 


039 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Prop. Pts. 



20 Table la — Condensed Logarithms and Antilogarithms [la 

CONDENSED LOGARITHMS TO FIFTEEN DECIMAL PLACES 

[The first digits of n are given in the first row at the top; the last digit of n in 
the left-hand column. The first column of logarithms are those of 1, 2, 3, •••, 9. 
The remaining columns give log (1 + x), where x = (0.1) fc times 1, 2, ••-, 9.] 



0^ 


First Digit 


1. 


1.0 


1.00 




Log n 


First Digits 

of log n >• 


.0 


.00 


1 
2 
3 
4 
5 
6 
7 
8 
9 


00000 00000 00000 
30102 99956 63981 
47712 12547 19662 
60205 99913 27962 
69897 00043 36019 
77815 12503 83644 
84509 80400 14257 
90308 99869 91944 
95424 25094 39325 


04139 26851 58225 
07918 12460 47625 
11394 33523 06837 
14612 80356 78238 
17609 12590 55681 
2041199826 55925 
23044 89213 78274 
25527 25051 03306 
27875 36009 52829 


0432 13737 82643 
0860 01717 61918 
1283 72247 05172 
1703 33392 98780 
2118 92990 69938 
2530 58652 64770 
2938 37776 85210 
3342 37554 86950 
3742 64979 40624 


043 40774 79319 
086 77215 31227 
130 09330 20418 
173 37128 09001 
216 60617 56508 
259 79807 19909 
302 94705 53618 
346 05321 09506 
389 11662 36911 



(continuation) 





1.000 


1.0000 


1.00000 


1.000000 


1.0000000 


1.00000000 


.000 


.0000 


.00000 


.000000 


.0000000 


.00000000 


1 

2 
3 
4 
5 
6 
7 
8 
9 


04 34272 76863 
08 68502 11649 
13 02688 05227 
17 36830 58465 
21 70929 72230 
26 04985 47390 
30 38997 84812 
34 72966 85364 
39 06892 49910 


43429 23104 

86858 02780 

1 30286 39028 

1 73714 31850 

2 17141 81245 

2 60568 87215 

3 03995 49761 
3 47421 68884 
3 90847 44584 


04342 94265 
08685 88095 
13028 81491 
17371 74453 
21714 66981 
26057 59074 
30400 50733 
34743 41958 
39086 32748 


0434 29446 
0868 58888 
1302 88325 
1737 17758 
2171 47187 
2605 76611 
3040 06031 
3474 35447 
3908 64858 


043 42945 
086 85890 
130 28834 
173 71779 
217 14724 
260 57668 
304 00613 
347 43557 
390 86502 


04 34294 
08 68589 
13 02883 
17 37178 
21 71472 
26 05767 
30 40061 
34 74356 
39 08650 



[For x < .00000001, log (1 + x) = x-M, to within 3 in the 17th place, where 
M = 0.43429448 • • • . Hence the last column gives multiples of M except for the 
decimal place. All the columns that would follow have the same significant digits 
displaced each time one place.] 



CONDENSED ANTILOGARITHMS TO TEN DECIMAL PLACES 

[The first digits of n are given in the first row at the top; n = (0.1) fc x; x = 1, 2, 
3, • • • , 9 are given in the left-hand column. The first digits in 10 n are given in the 
second row at the top.] 



X 


n = 0.1* 


O.Olz 


0.001a: 


O.OOOlx 


(0.1) 5 z 


(0.1) 6 x 


(0.1) 7 z 


1 

2 
3 
4 
5 
6 
7 
8 
9 


10* 


1. 


1.0 


1.00 


1.000 


1.0000 


1.00000 


1.25892 54118 
1.58489 31925 
1.99526 23150 
2.51188 64315 
3.16227 76602 
3.98107 17055 
5.01187 23363 
6.30957 34448 
7.94328 23472 


02329 29923 
04712 85481 
07151 93052 
09647 81961 
12201 84543 
14815 36215 
17489 75549 
20226 44346 
23026 87708 


0230 52381 
0461 57903 
0693 16689 
0925 28861 
1157 94543 
1391 13857 
1624 86929 
1859 13881 
2093 94837 


023 02850 
046 06231 
069 10142 
092 14583 
115 19555 
138 25058 
161 31092 
184 37657 
207 44753 


02 30261 
04 60528 
06 90799 
09 21076 
11 51359 
13 81646 
16 11939 
18 42238 
20 72541 


23026 
46052 
69078 

92104 

1 15130 
1 38156 
1 61182 

1 84209 

2 07235 


02303 
04605 
06908 
09210 
11513 
13816 
16118 
18421 
20723 



[For n < 0.000001, 10 n = 1 -f n- (1/M) to within 3 in the 12th decimal place, where 
(1/M) = 2.302585 • • ♦. Hence the last column gives multiples of (l/M) except for 
the decimal place. All the columns that would follow contain the same significant 
jdigits displaced one place for each new column.] 



TABLE II 



ACTUAL VALUES 



OF THE 



TRIGONOMETRIC FUNCTIONS 



FROM 



0° TO 90° AT INTERVALS OF ONE MINUTE 



TO 



FIVE DECIMAL PLACES 







T 




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17 




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Thus 2/ = sin a; g 


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UTtfi IK 


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T7ft l l 



21 



22 



0° — Values of Trigonometric Functions — 1' 



[II 



f 


Sin 


Tan 


Ctn 


Cos 







.00000 


.00000 




1.0000 


60 


1 


029 


029 


3437.7 


000 


59 


2 


058 


058 


1718.9 


000 


58 


3 


087 


087 


1145.9 


000 


5: 


4 


116 


116 


859.44 


000 


56 


5 


.00145 


.00145 


687.55 


1.0000 


55 


6 


175 


175 


572.96 


000 


54 


7 


204 


204 


491.11 


000 


53 


8 


233 


233 


429.72 


000 


52 


9 


262 


262 


381.97 


000 


51 


10 


.00291 


.00291 


343.77 


1.0000 


50 


11 


320 


320 


312.52 


.99999 


49 


12 


349 


349 


286.48 


999 


48 


13 


378 


378 


264.44 


999 


47 


14 


407 


407 


245.55 


999 


46 


15 


.00436 


.00436 


229.18 


.99999 


45 


16 


465 


465 


214.86 


999 


44 


17 


495 


495 


202.22 


999 


43 


18 


524 


524 


190.98 


999 


42 


19 


553 


553 


180.93 


998 


41 


20 


.00582 


.00582 


171.89 


.99998 


40 


21 


611 


611 


163.70 


998 


39 


22 


640 


640 


156.26 


998 


38 


23 


669 


669 


149.47 


998 


37 


24 


698 


698 


143.24 


998 


36 


25 


.00727 


.00727 


137.51 


.99997 


35 


26 


756 


756 


132.22 


997 


34 


27 


785 


785 


127.32 


997 


33 


28 


814 


815 


122.77 


997 


32 


29 


844 


844 


118.54 


996 


31 


30 


.00873 


.00873 


114.59 


.99996 


30 


31 


902 


902 


110.89 


996 


29 


32 


931 


931 


107.43 


996 


28 


33 


960 


960 


104.17 


995 


27 


34 


.00989 


.00989 


101.11 


995 


26 


35 


.01018 


.01018 


98.218 


.99995 


25 


36 


047 


047 


95.489 


995 


24 


37 


076 


076 


92.908 


994 


23 


38 


105 


105 


90.463 


994 


22 


39 


134 


135 


88.144 


994 


21 


40 


.01164 


.01164 


85.940 


.99993 


20 


41 


193 


193 


83.844 


993 


19 


42 


222 


222 


81.847 


993 


18 


43 


251 


251 


79.943 


992 


17 


44 


280 


280 


78.126 


992 


16 


45 


.01309 


.01309 


76.390 


.99991 


15 


46 


338 


338 


74.729 


991 


14 


47 


367 


367 


73.139 


991 


13 


48 


396 


396 


71.615 


990 


12 


49 


425 


425 


70.153 


990 


11 


50 


.01454 


.01455 


68.750 


.99989 


10 


51 


483 


484 


67.402 


989 


9 


52 


513 


513 


66.105 


989 


8 


53 


542 


542 


64.858 


988 


7 


54 


571 


571 


63.657 


988 


6 


55 


.01600 


.01600 


62.499 


.99987 


5 


56 


629 


629 


61.383 


987 


4 


57 


658 


658 


60.306 


986 


3 


58 


687 


687 


59.266 


986 


2 


59 


716 


716 


58.261 


985 


1 


60 


.01745 


.01746 


57.290 


.99985 





Cos 


Ctn 


Tan 


Sin 


/ 



i 


Sin 


Tan 


Ctn 


Cos 







.01745 


.01746 


57.290 


.99985 


60 


1 


774 


775 


56.351 


984 


59 


2 


803 


804 


55.442 


984 


58 


3 


832 


833 


54.561 


983 


57 


4 


862 


862 


53.709 


983 


56 


5 


.01891 


.01891 


52.882 


.99982 


55 


6 


920 


920 


52.081 


982 


54 


7 


949 


949 


51.303 


981 


53 


8 


.01978 


.01978 


50.549 


980 


52 


9 


.02007 


.02007 


49.816 


980 


51 


10 


.02036 


.02036 


49.104 


.99979 


50 


11 


065 


066 


48.412 


979 


49 


12 


094 


095 


47.740 


978 


48 


13 


123 


124 


47.085 


977 


47 


14 


152 


153 


46.449 


977 


46 


15 


.02181 


.02182 


45.829 


.99976 


45 


16 


211 


211 


45.226 


976 


44 


17 


240 


240 


44.639 


975 


43 


18 


269 


269 


44.066 


974 


42 


19 


298 


298 


43.508 


974 


41 


20 


.02327 


.02328 


42.964 


.99973 


40 


21 


356 


357 


42.433 


972 


39 


22 


385 


386 


41.916 


972 


38 


23 


414 


415 


41.411 


971 


37 


24 


443 


444 


40.917 


970 


36 


25 


.02472 


.02473 


40.436 


.99969 


35 


26 


501 


502 


39.965 


969 


34 


27 


530 


531 


39.506 


968 


33 


28 


560 


560 


39.057 


967 


32 


29 


589 


589 


38.618 


966 


31 


30 


.02618 


.02619 


38.188 


.99966 


30 


31 


647 


648 


37.769 


965 


29 


32 


676 


677 


37.358 


964 


28 


33 


705 


706 


36.956 


963 


27 


34 


734 


735 


36.563 


963 


26 


35 


.02763 


.02764 


36.178 


.99962 


25 


36 


792 


793 


35.801 


961 


24 


37 


821 


822 


35.431 


960 


23 


38 


850 


851 


35.070 


959 


22 


39 


879 


881 


34.715 


959 


21 


40 


.02908 


.02910 


34.368 


.99958 


20 


41 


938 


939 


34.027 


957 


19 


42 


967 


968 


33.694 


956 


18 


43 


.02996 


.02997 


33.366 


955 


17 


44 


.03025 


.03026 


33.045 


954 


16 


45 


.03054 


.03055 


32.730 


.99953 


15 


46 


083 


084 


32.421 


952 


14 


47 


112 


114 


32.118 


952 


13 


48 


141 


143 


31.821 


951 


12 


49 


170 


172 


31.528 


950 


11 


50 


.03199 


.03201 


31.242 


.99949 


10 


51 


228 


230 


30.960 


948 


9 


52 


257 


259 


30.683 


947 


8 


53 


286 


288 


30.412 


946 


7 


54 


316 


317 


30.145 


945 


6 


55 


.03345 


.03346 


29.882 


.99944 


5 


56 


374 


376 


29.624 


943 


4 


57 


403 


405 


29.371 


942 


3 


58 


432 


434 


29.122 


941 


2 


59 


461 


463 


28.877 


940 


1 


60 


.03490 


.03492 


28.636 


.99939 







Cos 


Ctn 


Tan 


Sin 


/ 



89' 



88° 



II] 



2° — Values of Trigonometric Functions — 3° 



23 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



Sin Tan Ctn Cos 



.03490 
519 

548 
577 
606 

.03635 
664 
693 
723 
752 

.03781 
810 
839 

868 
897 

.03926 

955 

.03984 

.04013 

042 

.04071 
100 
129 
159 

188 

.04217 
246 
275 
304 
333 

.04362 
391 
420 
449 
478 

.04507 
536 
565 
594 
623 

.04653 
682 
711 
740 
769 

.04798 
827 
856 
885 
914 

.04943 

.04972 

.05001 

030 

059 

.05088 
117 
146 
175 
205 

.05234 



.03492 
521 
550 
579 
609 

.03638 
667 
696 
725 
754 

.03783 
812 
842 
871 
900 

.03929 

958 

.03987 

.04016 

046 

.04075 
104 
133 
162 
191 

.04220 
250 
279 
308 
337 

.04366 
395 
424 
454 
483 

.04512 
541 
570 
599 
628 

.04658 

687 
716 
745 

774 

.04803 
833 
862 
891 
920 

.04949 

.04978 

.05007 

037 

066 

.05095 
124 
153 
182 
212 

.05241 



28.636 

.399 

28.166 

27.937 

.712 

27.490 

.271 
27.057 
26.845 

.637 
26.432 

.230 
26.031 
25.835 

.642 

25.452 

.264 
25.080 
24.898 

.719 
24.542 

.368 

.196 
24.026 
23.859 

23.695 

.532 

.372 

.214 

23.058 

22.904 

.752 

.602 

.454 

.308 

22.164 

22.022 

21.881 

.743 

.606 

21.470 

.337 

.205 

21.075 

20.946 

20.819 
.693 
.569 
.446 
.325 

20.206 

20.087 

19.970 

.855 

.740 

19.627 

.516 

.405 

.296 

.188 

19.081 



.99939 
938 
937 
936 
935 

.99934 
933 
932 
931 
930 

.99929 
927 
926 
925 
924 

.99923 
922 
921 
919 
918 

.99917 
916 
915 
913 
912 

.99911 
910 
909 
907 
906 

.99905 
904 
902 
901 
900 

.99898 
897 
896 
894 
893 

.99892 
890 
889 
888 
886 

.99885 
883 
882 
881 
879 

.99878 
876 
875 
873 

872 

.99870 
869 
867 
866 
864 

.99863 



Cos Ctn Tan Sin 

87° 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




/ 


Sin 


Tan 


Ctn 


Cos 







.05234 


.05241 


19.081 


.99863 


60 


1 


263 


270 


18.976 


861 


59 


2 


292 


299 


.871 


860 


58 


3 


321 


328 


.768 


858 


57 


4 


350 


357 


.666 


857 


56 


5 


.05379 


.05387 


18.564 


.99855 


55 


6 


408 


416 


.464 


854 


54 


7 


437 


445 


.366 


852 


53 


8 


466 


474 


.268 


851 


52 


9 


495 


503 


.171 


849 


51 


10 


.05524 


.05533 


18.075 


.99847 


50 


11 


553 


562 


17.980 


846 


49 


12 


582 


591 


.886 


844 


48 


13 


611 


620 


.793 


842 


47 


14 


640 


649 


.702 


841 


46 


15 


.05669 


.05678 


17.611 


.99839 


45 


16 


698 


708 


.521 


838 


44 


17 


727 


737 


.431 


836 


43 


18 


756 


766 


.343 


834 


42 


19 


785 


795 


.256 


833 


41 


20 


.05814 


.05824 


17.169 


.99831 


40 


21 


844 


854 


17.084 


829 


39 


22 


873 


883 


16.999 


827 


38 


23 


902 


912 


.915 


826 


37 


24 


931 


941 


.832 


824 


36 


25 


.05960 


.05970 


16.750 


.99822 


35 


26 


.05989 


.05999 


.668 


821 


34 


27 


.06018 


.06029 


.587 


819 


33 


28 


047 


058 


.507 


817 


32 


29 


076 


087 


.428 


815 


31 


30 


.06105 


.06116 


16.350 


.99813 


30 


31 


134 


145 


.272 


812 


29 


32 


163 


175 


.195 


810 


28 


33 


192 


204 


.119 


808 


27 


34 


221 


233 


16.043 


806 


26 


35 


.06250 


.06262 


15.969 


.99804 


25 


36 


279 


291 


.895 


803 


24 


37 


308 


321 


.821 


801 


23 


38 


337 


350 


.748 


799 


22 


39 


366 


379 


.676 


797 


21 


40 


.06395 


.06408 


15.605 


.99795 


20 


41 


424 


438 


.534 


793 


19 


42 


453 


467 


.464 


792 


18 


43 


482 


496 


.394 


790 


17 


44 


511 


525 


.325 


788 


16 


45 


.06540 


.06554 


15.257 


.99786 


15 


46 


569 


584 


.189 


784 


14 


47 


598 


613 


.122 


782 


13 


48 


627 


642 


15.056 


780 


12 


49 


656 


671 


14.990 


778 


11 


50 


.06685 


.06700 


14.924 


.99776 


10 


51 


714 


730 


.860 


774 


9 


52 


743 


759 


.795 


772 


8 


53 


773 


788 


.732 


770 


7 


54 


802 


817 


.669 


768 


6 


55 


.06831 


.06847 


14.606 


.99766 


5 


56 


860 


876 


.544 


764 


4 


57 


889 


905 


.482 


762 


3 


58 


918 


934 


.421 


760 


2 


59 


947 


963 


.361 


758 


1 


60 


.06976 


.06993 


14.301 


.99756 







Cos 


Ctn 


Tan 


Sin 


/ 



86< 



24 



4° — Values of Trigonometric Functions — 5' 



[II 



/ 


Sin 


Tan 


Ctn 


Cos 







.06976 


.06993 


14.301 


.99756 


60 


1 


.07005 


.07022 


.241 


754 


59 


2 


034 


051 


.182 


752 


5S 


3 


063 


080 


.124 


750 


57 


4 


092 


110 


.065 


748 


56 


5 


.07121 


.07139 


14.008 


.99746 


55 


6 


150 


168 


13.951 


744 


54 


7 


179 


197 


.894 


742 


53 


8 


208 


227 


.838 


740 


52 


9 


237 


256 


.782 


738 


51 


10 


.07266 


.07285 


13.727 


.99736 


50 


11 


295 


314 


.672 


734 


49 


12 


324 


344 


.617 


731 


48 


13 


353 


373 


.563 


729 


47 


14 


382 


402 


.510 


727 


46 


15 


.07411 


.07431 


13.457 


.99725 


45 


16 


440 


461 


.404 


723 


44 


17 


469 


490 


.352 


721 


43 


18 


498 


519 


.300 


719 


42 


19 


527 


548 


.248 


716 


41 


20 


.07556 


.07578 


13.197 


.99714 


40 


21 


585 


607 


.146 


712 


39 


22 


614 


636 


.096 


710 


38 


23 


643 


665 


13.046 


708 


37 


24 


672 


695 


12.996 


705 


36 


25 


.07701 


.07724 


12.947 


.99703 


35 


26 


730 


753 


.898 


701 


34 


27 


759 


782 


.850 


699 


33 


28 


788 


812 


.801 


696 


32 


29 


817 


841 


.754 


694 


31 


30 


.07846 


.07870 


12.706 


.99692 


30 


31 


875 


899 


.659 


689 


29 


32 


904 


929 


.612 


687 


28 


33 


933 


958 


.566 


685 


27 


34 


962 


.07987 


.520 


683 


26 


35 


.07991 


.08017 


12.474 


.99680 


25 


36 


.08020 


046 


.429 


678 


24 


37 


049 


075 


.384 


676 


23 


38 


078 


104 


.339 


673 


22 


39 


107 


134 


.295 


671 


21 


40 


.08136 


.08163 


12.251 


.99668 


20 


41 


165 


192 


.207 


666 


19 


42 


194 


221 


.163 


664 


18 


43 


223 


251 


.120 


661 


17 


44 


252 


280 


.077 


659 


16 


45 


.08281 


.08309 


12.035 


.99657 


15 


46 


310 


339 


11.992 


654 


14 


47 


339 


368 


.950 


652 


13 


48 


368 


397 


.909 


649 


12 


49 


397 


427 


.867 


647 


11 


50 


.08426 


.08456 


11.826 


.99644 


10 


51 


455 


485 


.785 


642 


9 


52 


484 


514 


.745 


639 


8 


53 


513 


544 


.705 


637 


7 


54 


542 


573 


.664 


635 


6 


55 


.08571 


.08602 


11.625 


.99632 


5 


56 


600 


632 


.585 


630 


4 


57 


629 


661 


.546 


627 


3 


58 


658 


690 


.507 


625 


2 


59 


687 


720 


.468 


622 


1 


60 


.08716 


.08749 


11.430 


.99619 







Cos 


Ctn 


Tan 


Sin 


1 





1 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 

54 

55 

56 
57 

58 
59 

60 



Sin Tan Ctn Cos 



.08716 
745 
774 
803 
831 

.08860 
889 
918 
947 

.08976 

.09005 
034 
063 
092 
121 

.09150 
179 
208 
237 
266 

.09295 
324 
353 

382 
411 

.09440 
469 
498 
527 
556 

.09585 
614 
642 
671 
700 

.09729 
758 
787 
816 
845 

.09874 
903 
932 
961 

.09990 

.10019 
048 
077 
106 
135 

.10164 
192 
221 
250 
279 

.10308 
337 
366 
395 
424 

.10453 



Cos 



.08749 
778 
807 
837 
866 

.08895 

925 

954 

.08983 

.09013 

.09042 

071 

101 

130 

159 

.09189 

218 
247 
277 
306 

.09335 
365 
394 
423 
453 

.09482 
511 
541 
570 
600 

.09629 
658 

688 
717 
746 

.09776 
805 
834 
864 
893 

.09923 

952 

.09981 

.10011 

040 

.10069 
099 
128 
158 

187 

.10216 
246 
275 
305 
334 

.10363 
393 
422 
452 
481 

.10510 



11.430 
.392 
.354 
.316 
.279 

11.242 
.205 
.168 
.132 
.095 

11.059 

11.024 

10.988 

.953 

.918 

10.883 

.848 

• .814 

.780 

.746 

10.712 

.678 

.645 

.612 

.579 

10.546 
.514 

.481 
.449 
.417 

10.385 
.354 
.322 
.291 
.260 

10.229 
.199 
.168 
.138 
.108 

10.078 

.048 

10.019 

9.9893 

.9601 

9.9310 
.9021 
.8734 

.8448 
.8164 

9.7882 
.7601 
.7322 
.7044 
.6768 

9.6493 
.6220 
.5949 
.5679 
.5411 

9.5144 



85< 



Ctn Tan 

84° 



.99619 
617 
614 
612 
609 

.99607 
604 
602 
599 
596 

.99594 
591 
588 
586 
583 

.99580 
578 
575 
572 
570 

.99567 
564 
562 
559 
556 

.99553 
551 
548 
545 
542 

.99540 
537 
534 
531 

528 

.99526 
523 
520 
517 
514 

.99511 
508 
506 
503 
500 

.99497 
494 
491 
488 
485 

.99482 
479 
476 
473 
470 

.99467 
464 
461 
458 
455 

.99452 



Sin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 




II] 



Values of Trigonometric Functions — 7' 



25 



f 


Sin 


Tan 


Ctn 


Cos 







.10453 


.10510 


9.5144 


.99452 


60 


1 


482 


540 


.4878 


449 


59 


2 


511 


569 


.4614 


446 


58 


3 


540 


599 


.4352 


443 


57 


4 


569 


628 


.4090 


440 


56 


5 


.10597 


.10657 


9.3831 


.99437 


55 


6 


626 


687 


.3572 


434 


54 


7 


655 


716 


.3315 


431 


53 


8 


684 


746 


.3060 


428 


52 


9 


713 


775 


.2806 


424 


51 


10 


.10742 


.10805 


9.2553 


.99421 


50 


11 


771 


834 


.2302 


418 


49 


12 


800 


863 


.2052 


415 


48 


13 


829 


893 


.1803 


412 


47 


14 


858 


922 


.1555 


409 


46 


15 


.10887 


.10952 


9.1309 


.99406 


45 


16 


916 


.10981 


.1065 


402 


44 


17 


945 


.11011 


.0821 


399 


43 


18 


.10973 


040 


.0579 


396 


42 


19 


.11002 


070 


.0338 


393 


41 


20 


.11031 


.11099 


9.0098 


.99390 


40 


21 


060 


128 


8.9860 


386 


39 


22 


089 


158 


.9623 


383 


38 


23 


118 


• 187 


.9387 


380 


37 


24 


147 


217 


.9152 


377 


36 


25 


.11176 


.11246 


8.8919 


.99374 


35 


26 


205 


276 


.8686 


370 


34 


27 


234 


305 


.8455 


367 


33 


28 


263 


335 


.8225 


364 


32 


29 


291 


364 


.7996 


360 


31 


30 


.11320 


.11394 


8.7769 


.99357 


30 


31 


349 


423 


.7542 


354 


29 


32 


378 


452 


.7317 


351 


28 


33 


407 


482 


.7093 


347 


27 


34 


436 


511 


.6870 


344 


26 


35 


.11465 


.11541 


8.6648 


.99341 


25 


36 


494 


570 


.6427 


337 


24 


37 


523 


600 


.6208 


334 


23 


38 


552 


629 


.5989 


331 


22 


39 


580 


659 


.5772 


327 


21 


40 


.11609 


.11688 


8.5555 


.99324 


20 


41 


638 


718 


.5340 


320 


19 


42 


667 


747 


.5126 


317 


18 


43 


696 


777 


.4913 


314 


17 


44 


725 


806 


.4701 


310 


16 


45 


.11754 


.11836 


8.4490 


.99307 


15 


46 


783 


865 


.4280 


303 


14 


47 


812 


895 


.4071 


300 


13 


48 


840 


924 


.3863 


297 


12 


49 


869 


954 


.3656 


293 


11 


50 


.11898 


.11983 


8.3450 


.99290 


10 


51 


927 


.12013 


.3245 


286 


9 


52 


956 


042 


.3041 


283 


8 


53 


.11985 


072 


.2838 


279 


7 


54 


.12014 


101 


.2636 


276 


6 


55 


.12043 


.12131 


8.2434 


.99272 


5 


56 


071 


160 


.2234 


269 


4 


57 


100 


190 


.2035 


265 


3 


58 


129 


219 


.1837 


262 


2 


59 


158 


249 


.1640 


258 


1 


60 


.12187 


.12278 


8.1443 


.99255 







Cos 


Ctn 


Tan 


Sin 


/ 





1 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



Sin Tan Ctn Cos 



.12187 
216 
245 
274 
302 

.12331 
360 
389 
418 

447 

.12476 
504 
533 
562 
591 

.12620 
649 
678 
706 
735 

.12764 
793 
822 
851 
880 

.12908 

937 

966 

.12995 

.13024 

.13053 
081 
110 
139 
168 

.13197 
226 
254 
283 
312 

.13341 
370 
399 

427 
456 

.13485 
514 
543 
572 

600 

.13629 
658 

687 
716 
744 

.13773 

802 
831 
860 
889 

.13917 



12278 
308 
338 
367 
397 

.12426 
456 
485 
515 
544 

.12574 
603 
633 
662 
692 

.12722 
751 

781 
810 
840 

.12869 
899 
929 
958 

.12988 

.13017 
047 
076 
106 
136 

.13165 
195 
224 
254 

284 

.13313 
343 
372 
402 
432 

.13461 
491 
521 
550 

580 

.13609 
639 
669 

698 

728 

.13758 

787 
817 
846 
876 

.13906 

935 

965 

.13995 

.14024 

.14054 



8.1443 
.1248 
.1054 
.0860 
.0667 

8.0476 

.0285 

8.0095 

7.9906 

.9718 

7.9530 
.9344 
.9158 
.8973 

.8789 

7.8606 
.8424 
.8243 
.8062 

.7882 

7.7704 
.7525 
.7348 
.7171 
.6996 

7.6821 
.6647 
.6473 
.6301 
.6129 

7.5958 
.5787 
.5618 
.5449 
.5281 

7.5113 

.4947 
.4781 
.4615 
.4451 

7.4287 
.4124 
.3962 
.3800 
.3639 

7.3479 
.3319 
.3160 
.3002 

.2844 

7.2687 
.2531 
.2375 
.2220 
.2066 

7.1912 
.1759 
.1607 
.1455 
.1304 

7.1154 



.99255 
251 
248 
244 
240 

.99237 
233 
230 
226 
222 

.99219 
215 
211 

208 
204 

.99200 
197 
193 
189 
186 

.99182 
178 
175 
171 
167 

.99163 
160 
156 
152 
148 

.99144 
141 
137 
133 
129 

.99125 
122 
118 
114 
110 

.99106 
102 
098 
094 
091 

.99087 
083 
079 
075 
071 

.99067 
063 
059 
055 
051 

.99047 
043 
039 
035 
031 

.99027 



83° 



Cos Ctn Tan Sin 

82° 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





26 



8° — Values of Trigonometric Functions — 9' 



[II 



/ 


Sin 


Tan 


Ctn 


Cos 







.13917 


.14054 


7.1154 


.99027 


60 


1 


946 


084 


.1004 


023 


59 


2 


.13975 


113 


.0855 


019 


58 


3 


.14004 


143 


.0706 


015 


57 


4 


033 


173 


.0558 


011 


56 


5 


.14061 


.14202 


7.0410 


.99006 


55 


6 


090 


232 


.0264 


.99002 


54 


7 


119 


262 


7.0117 


.98998 


53 


8 


148 


291 


6.9972 


994 


52 


9 


177 


321 


.9827 


990 


51 


10 


.14205 


.14351 


6.9682 


.98986 


50 


11 


234 


381 


.9538 


982 


49 


12 


263 


410 


.9395 


978 


48 


13 


292 


440 


.9252 


973 


47 


14 


320 


470 


.9110 


969 


46 


15 


.14349 


.14499 


6.8969 


.98965 


45 


16 


378 


529 


.8828 


961 


44 


17 


407 


559 


.8687 


957 


43 


18 


436 


588 


.8548 


953 


42 


19 


464 


618 


.8408 


948 


41 


20 


.14493 


.14648 


6.8269 


.98944 


40 


21 


522 


678 


.8131 


940 


39 


22 


551 


707 


.7994 


936 


38 


23 


580 


737 


.7856 


931 


37 


24 


608 


767 


.7720 


927 


36 


25 


.14637 


.14796 


6.7584 


.98923 


35 


26 


666 


826 


.7448 


919 


34 


27 


695 


856 


.7313 


914 


33 


28 


723 


886 


.7179 


910 


32 


29 


752 


915 


.7045 


906 


31 


30 


.14781 


.14945 


6.6912 


.98902 


30 


31 


810 


.14975 


.6779 


897 


29 


32 


838 


.15005 


.6646 


893 


28 


33 


867 


034 


.6514 


889 


27 


34 


896 


064 


.6383 


884 


26 


35 


.14925 


.15094 


6.6252 


.98880 


25 


36 


954 


124 


.6122 


876 


24 


37 


.14982 


153 


.5992 


871 


23 


38 


.15011 


183 


.5863 


867 


22 


39 


040 


213 


.5734 


863 


21 


40 


.15069 


.15243 


6.5606 


.98858 


20 


41 


097 


272 


.5478 


854 


19 


42 


126 


302 


.5350 


849 


18 


43 


155 


332 


.5223 


845 


17 


44 


184 


362 


.5097 


841 


16 


45 


.15212 


.15391 


6.4971 


.98836 


15 


46 


241 


421 


.4846 


832 


14 


47 


270 


451 


.4721 


827 


13 


48 


299 


481 


.4596 


823 


12 


49 


327 


511 


.4472 


818 


11 


50 


.15356 


.15540 


6.4348 


.98814 


10 


51 


385 


570 


.4225 


809 


9 


52 


414 


600 


.4103 


805 


8 


53 


442 


630 


.3980 


800 


7 


54 


471 


660 


.3859 


796 


6 


55 


.15500 


.15689 


6.3737 


.98791 


5 


56 


529 


719 


.3617 


787 


4 


57 


557 


749 


.3496 


782 


3 


58 


586 


779 


.3376 


778 


2 


59 


615 


809 


.3257 


773 


1 


60 


.15643 


.15838 


6.3138 


.98769 







Cos 


Ctn 


Tan 


Sin 


/ 



/ 


Sin 


Tan 


Ctn 


Cos 







.15643 


.15838 


6.3138 


.98769 


60 


1 


672 


868 


.3019 


764 


59 


2 


701 


898 


.2901 


760 


58 


3 


730 


928 


.2783 


755 


57 


4 


758 


958 


.2666 


751 


56 


5 


.15787 


.15988 


6.2549 


.98746 


55 


6 


816 


.16017 


.2432 


741 


54 


7 


845 


047 


.2316 


737 


53 


8 


873 


077 


.2200 


732 


52 


9 


902 


107 


.2085 


728 


51 


10 


.15931 


.16137 


6.1970 


.98723 


50 


11 


959 


167 


.1856 


718 


49 


12 


.15988 


196 


.1742 


714 


48 


13 


.16017 


226 


.1628 


709 


47 


14 


046 


256 


.1515 


704 


46 


15 


.16074 


.16286 


6.1402 


.98700 


45 


16 


103 


316 


.1290 


695 


44 


17 


132 


346 


.1178 


690 


43 


18 


160 


376 


.1066 


686 


42 


19 


189 


405 


.0955 


681 


41 


20 


.16218 


.16435 


6.0844 


.98676 


40 


21 


246 


465 


.0734 


671 


39 


22 


275 


495 


.0624 


667 


38 


23 


304 


525 


.0514 


662 


37 


24 


333 


555 


.0405 


657 


36 


25 


.16361 


.16585 


6.0296 


.98652 


35 


26 


390 


615 


.0188 


648 


34 


27 


419 


645 


6.0080 


643 


33 


28 


447 


674 


5.9972 


638 


32 


29 


476 


704 


.9865 


633 


31 


30 


.16505 


.16734 


5.9758 


.98629 


30 


31 


533 


764 


.9651 


624 


29 


32 


562 


794 


.9545 


619 


28 


33 


591 


824 


.9439 


614 


27 


34 


620 


854 


.9333 


609 


26 


35 


.16648 


.16884 


5.9228 


.98604 


25 


36 


677 


914 


.9124 


600 


24 


37 


706 


944 


.9019 


595 


23 


38 


734 


.16974 


.8915 


590 


22 


39 


763 


.17004 


.8811 


585 


21 


40 


.16792 


.17033 


5.8708 


.98580 


20 


41 


820 


063 


.8605 


575 


19 


42 


849 


093 


.8502 


570 


18 


43 


878 


123 


.8400 


565 


17 


44 


906 


153 


.8298 


561 


16 


45 


.16935 


.17183 


5.8197 


.98556 


15 


46 


964 


213 


.8095 


551 


14 


47 


.16992 


243 


.7994 


546 


13 


48 


.17021 


273 


.7894 


541 


12 


49 


050 


303 


.7794 


536 


11 


50 


.17078 


.17333 


5.7694 


.98531 


10 


51 


107 


363 


.7594 


526 


9 


52 


136 


393 


.7495 


521 


8 


53 


164 


423 


.7396 


516 


7 


54 


193 


453 


.7297 


511 


6 


55 


.17222 


.17483 


5.7199 


.98506 


5 


56 


250 


513 


.7101 


501 


4 


57 


279 


543 


.7004 


496 


3 


58 


308 


573 


.6906 


491 


2 


59 


336 


603 


.6809 


486 


1 


60 


.17365 


.17633 


5.6713 


.98481 







Cos 


Ctn 


Tan 


Sin 


/ 



81° 



80° 



II] 10° — Values of Trigonometric Functions — 11' 



27 



/ 


Sin 


Tan 


Ctn 


Cos 







.17365 


.17633 


5.6713 


.98481 


60 


1 


393 


663 


.6617 


476 


59 


2 


422 


693 


.6521 


471 


58 


3 


451 


723 


.6425 


466 


57 


4 


479 


753 


.6329 


461 


56 


5 


.17508 


.17783 


5.6234 


.98455 


55 


6 


537 


813 


.6140 


450 


54 


7 


565 


843 


.6045 


445 


53 


8 


594 


873 


.5951 


440 


52 


9 


623 


903 


.5857 


435 


51 


10 


.17651 


.17933 


5.5764 


.98430 


50 


11 


680 


963 


.5671 


425 


49 


12 


708 


.17993 


.5578 


420 


48 


13 


737 


.18023 


.5485 


414 


47 


14 


766 


053 


.5393 


409 


46 


15 


.17794 


.18083 


5.5301 


.98404 


45 


16 


823 


113 


.5209 


399 


44 


17 


852 


143 


.5118 


394 


43 


18 


880 


173 


.5026 


389 


42 


19 


909 


203 


.4936 


383 


41 


20 


.17937 


.18233 


5.4845 


.98378 


40 


21 


966 


263 


.4755 


373 


39 


22 


.17995 


293 


.4665 


368 


38 


23 


.18023 


323 


.4575 


362 


37 


24 


052 


353 


.4486 


357 


36 


25 


.18081 


.18384 


5.4397 


.98352 


35 


26 


109 


414 


.4308 


347 


34 


27 


138 


444 


.4219 


341 


33 


28 


166 


474 


.4131 


336 


32 


29 


195 


504 


.4043 


331 


31 


30 


.18224 


.18534 


5.3955 


.98325 


30 


31 


252 


564 


.3868 


320 


29 


32 


281 


594 


.3781 


315 


28 


33 


309 


624 


.3694 


310 


27 


34 


338 


654 


.3607 


304 


26 


35 


.18367 


.18684 


5.3521 


.98299 


25 


36 


395 


714 


.3435 


294 


24 


37 


424 


745 


.3349 


288 


23 


38 


452 


775 


.3263 


283 


22 


39 


481 


805 


.3178 


277 


21 


40 


.18509 


.18835 


5.3093 


.98272 


20 


41 


538 


865 


.3008 


267 


19 


42 


567 


895 


.2924 


261 


18 


43 


595 


925 


.2839 


256 


17 


44 


624 


955 


.2755 


250 


16 


45 


.18652 


.18986 


5.2672 


.98245 


15 


46 


681 


.19016 


.2588 


240 


14 


47 


710 


046 


.2505 


234 


13 


48 


738 


076 


.2422 


229 


12 


49 


767 


106 


.2339 


223 


11 


50 


.18795 


.19136 


5.2257 


.98218 


10 


51 


824 


166 


.2174 


212 


9 


52 


852 


197 


.2092 


207 


8 


53 


881 


227 


.2011 


201 


7 


54 


910 


257 


.1929 


196 


6 


55 


.18938 


.19287 


5.1848 


.98190 


5 


56 


967 


317 


.1767 


185 


4 


57 


.18995 


347 


.1686 


179 


3 


58 


.19024 


378 


.1606 


174 


2 


59 


052 


408 


.1526 


168 


1 


60 


.19081 


.19438 


5.1446 


.98163 





I Cos 


Ctn 


Tan 


Sin 


/ 



/ 


Sin 


Tan 


Ctn 


Cos 







.19081 


.19438 


5.1446 


.98163 


60 


1 


109 


468 


.1366 


157 


59 


2 


138 


498 


.1286 


152 


58 


3 


167 


529 


.1207 


146 


57 


4 


195 


559 


.1128 


140 


56 


5 


.19224 


.19589 


5.1049 


.98135 


55 


6 


252 


619 


.0970 


129 


54 


7 


281 


649 


.0892 


124 


53 


8 


309 


680 


.0814 


118 


52 


9 


338 


710 


.0736 


112 


51 


10 


.19366 


.19740 


5.0658 


.98107 


50 


11 


395 


770 


.0581 


101 


49 


12 


423 


801 


.0504 


096 


48 


13 


452 


831 


.0427 


090 


47 


14 


481 


861 


.0350 


084 


46 


15 


.19509 


.19891 


5.0273 


.98079 


45 


16 


538 


921 


.0197 


073 


44 


17 


566 


952 


.0121 


067 


43 


18 


595 


.19982 


5.0045 


061 


42 


19 


623 


.20012 


4.9969 


056 


41 


20 


.19652 


.20042 


4.9894 


.98050 


40 


21 


680 


073 


.9819 


044 


39 


22 


709 


103 


.9744 


039 


38 


23 


737 


133 


.9669 


033 


37 


24 


766 


164 


.9594 


027 


36 


25 


.19794 


.20194 


4.9520 


.98021 


35 


26 


823 


224 


.9446 


016 


34 


27 


851 


254 


.9372 


010 


33 


28 


880 


285 


.9298 


.98004 


32 


29 


908 


315 


.9225 


.97998 


31 


30 


.19937 


.20345 


4.9152 


.97992 


30 


31 


965 


376 


.9078 


987 


29 


32 


.19994 


406 


.9006 


981 


28 


33 


.20022 


436 


.8933 


975 


27 


34 


051 


466 


.8860 


969 


26 


35 


.20079 


.20497 


4.8788 


.97963 


25 


36 


108 


527 


.8716 


958 


24 


37 


136 


557 


.8644 


952 


23 


38 


165 


588 


.8573 


946 


22 


39 


193 


618 


.8501 


940 


21 


40 


.20222 


.20648 


4.8430 


.97934 


20 


41 


250 


679 


.8359 


928 


19 


42 


279 


709 


.8288 


922 


18 


43 


307 


739 


.8218 


916 


17 


44 


336 


770 


.8147 


910 


16 


45 


.20364 


.20800 


4.8077 


.97905 


15 


46 


393 


830 


.8007 


899 


14 


47 


421 


861 


.7937 


893 


13 


48 


450 


891 


.7867 


887 


12 


49 


478 


921 


.7798 


881 


11 


50 


.20507 


.20952 


4.7729 


.97875 


10 


51 


535 


.20982 


.7659 


869 


9 


52 


563 


.21013 


.7591 


863 


8 


53 


592 


043 


.7522 


857 


7 


54 


620 


073 


.7453 


851 


6 


55 


.20649 


.21104 


4.7385 


.97845 


5 


56 


677 


134 


.7317 


839 


4 


57 


706 


164 


.7249 


833 


3 


58 


734 


195 


.7181 


827 


2 


59 


763 


225 


.7114 


821 


1 


60 


.20791 


.21256 


4.7046 


.97815 







Cos 


Ctn 


Tan 


Sin 


t 



79' 



78° 



28 


12° — Values of Trigonometric Functions — 13° 


[II 


/ 


Sin 


Tan 


Ctn 


Cos 




_ 


Sin 


Tan 


Ctn 


Cos 







.20791 


.21256 


4.7046 


.97815 


60 





.22495 


.23087 


4.3315 


.97437 


60 


1 


820 


286 


.6979 


809 


59 


1 


523 


117 


.3257 


430 


59 


2 


848 


316 


.6912 


803 


58 


2 


552 


148 


.3200 


424 


58 


3 


877 


347 


.6845 


797 


57 


3 


580 


179 


.3143 


417 


57 


4 


905 


377 


.6779 


791 


56 


4 


608 


209 


.3086 


411 


56 


5 


.20933 


.21408 


4.6712 


.97784 


55 


5 


.22637 


.23240 


4.3029 


.97404 


55 


6 


962 


438 


.6646 


778 


54 


6 


665 


271 


.2972 


398 


54 


7 


.20990 


469 


.6580 


772 


53 


7 


693 


301 


.2916 


391 


53 


8 


.21019 


499 


.6514 


766 


52 


8 


722 


332 


.2859 


384 


52 


9 


047 


529 


.6448 


760 


51 


9 


750 


363 


.2803 


378 


51 


10 


.21076 


.21560 


4.6382 


.97754 


50 


10 


.22778 


.23393 


4.2747 


.97371 


50 


11 


104 


590 


.6317 


748 


49 


11 


807 


424 


.2691 


365 


49 


12 


132 


621 


.6252 


742 


48 


12 


835 


455 


.2635 


358 


48 


13 


161 


651 


.6187 


735 


47 


13 


863 


485 


.2580 


351 


47 


14 


189 


682 


.6122 


729 


46 


14 


892 


516 


.2524 


345 


46 


15 


.21218 


.21712 


4.6057 


.97723 


45 


15 


.22920 


.23547 


4.2468 


.97338 


45 


16 


246 


743 


.5993 


717 


44 


16 


948 


578 


.2413 


331 


44 


17 


275 


773 


.5928 


711 


43 


17 


.22977 


608 


.2358 


325 


43 


18 


303 


804 


.5864 


705 


42 


18 


.23005 


639 


.2303 


318 


42 


19 


331 


834 


.5800 


698 


41 


19 


033 


670 


.2248 


311 


41 


20 


.21360 


.21864 


4.5736 


.97692 


40 


20 


.23062 


.23700 


4.2193 


.97304 


40 


21 


388 


895 


.5673 


686 


39 


21 


090 


731 


.2139 


298 


39 


22 


417 


925 


.5609 


680 


38 


22 


118 


762 


.2084 


291 


38 


23 


445 


956 


.5546 


673 


37 


23 


146 


793 


.2030 


284 


37 


24 


474 


.21986 


.5483 


667 


36 


24 


175 


823 


.1976 


278 


36 


25 


.21502 


.22017 


4.5420 


.97661 


35 


25 


.23203 


.23854 


4.1922 


.97271 


35 


26 


530 


047 


.5357 


655 


34 


26 


231 


885 


.1868 


264 


34 


27 


559 


078 


.5294 


648 


33 


27 


260 


916 


.1814 


257 


33 


28 


587 


108 


.5232 


642 


32 


28 


288 


946 


.1760 


251 


32 


29 


616 


139 


.5169 


636 


31 


29 


316 


.23977 


.1706 


244 


31 


30 


.21644 


.22169 


4.5107 


.97630 


30 


30 


.23345 


.24008 


4.1653 


.97237 


30 


31 


672 


200 


.5045 


623 


29 


31 


373 


039 


.1600 


230 


29 


32 


701 


231 


.4983 


617 


28 


32 


401 


069 


.1547 


223 


28 


33 


729 


261 


.4922 


611 


27 


33 


429 


100 


.1493 


217 


27 


34 


758 


292 


.4860 


604 


26 


34 


458 


131 


.1441 


210 


26 


35 


.21786 


.22322 


4.4799 


.97598 


25 


35 


.23486 


.24162 


4.1388 


.97203 


25 


36 


814 


353 


.4737 


592 


24 


36 


514 


193 


.1335 


196 


24 


37 


843 


383 


.4676 


585 


23 


37 


542 


223 


.1282 


189 


23 


38 


871 


414 


.4615 


579 


22 


38 


571 


254 


.1230 


182 


22 


39 


899 


444 


.4555 


573 


21 


39 


599 


285 


.1178 


176 


21 


40 


.21928 


.22475 


4.4494 


.97566 


20 


40 


.23627 


.24316 


4.1126 


.97169 


20 


41 


956 


505 


.4434 


560 


19 


41 


656 


347 


.1074 


162 


19 


42 


.21985 


536 


.4373 


553 


18 


42 


684 


377 


.1022 


155 


18 


43 


.22013 


567 


.4313 


547 


17 


43 


712 


408 


.0970 


148 


17 


44 


041 


597 


.4253 


541 


16 


44 


740 


439 


.0918 


141 


16 


45 


.22070 


.22628 


4.4194 


.97534 


15 


45 


.23769 


.24470 


4.0867 


.9^134 


15 


46 


098 


658 


.4134 


528 


14 


46 


797 


501 


.0815 


127 


14 


47 


126 


689 


.4075 


521 


13 


47 


825 


532 


.0764 


120 


13 


48 


155 


719 


.4015 


515 


12 


48 


853 


562 


.0713 


113 


12 


49 


183 


750 


,3956 


508 


11 


49 


882 


593 


.0662 


106 


11 


50 


.22212 


.22781 


4.3897 


.97502 


10 


50 


.23910 


.24624 


4.0611 


.97100 


10 


51 


240 


811 


.3838 


496 


9 


51 


938 


655 


.0560 


093 


9 


52 


268 


842 


.3779 


489 


8 


52 


966 


686 


.0509 


086 


8 


53 


297 


872 


.3721 


483 


7 


53 


.23995 


717 


.0459 


079 


7 


54 


325 


903 


.3662 


476 


6 


54 


.24023 


747 


.0408 


072 


6 


55 


.22353 


.22934 


4.3604 


.97470 


5 


55 


.24051 


.24778 


4.0358 


.97065 


5 


56 


382 


964 


.3546 


463 


4 


56 


079 


809 


.0308 


058 


4 


57 


410 


.22995 


.3488 


457 


3 


57 


108 


840 


.0257 


051 


3 


58 


438 


.23026 


.3430 


450 


2 


58 


136 


871 


.0207 


044 


2 


59 


467 


056 


.3372 


444 


1 


59 


164 


902 


.0158 


037 


1 


60 


.22495 


.23087 


4.3315 


.97437 





60 


.24192 


.24933 


4.0108 


.97030 







Cos 


Ctn 


Tan 


Sin 


i 




Cos 


Ctn 


Tan 


Sin 


/ 



IT 



76° 



II] 


14° — Values of Trigonometric Functions — 15° 


29 


/ 


Sin 


Tan 


Ctn 


Cos 


60 


/ 


Sin 


Tan 


Ctn 


Cos 


~60 





.24192 


.24933 


4.0108 


.97030 





.25882 


.26795 


3.7321 


.96593 


1 


220 


964 


.0058 


023 


59 


1 


910 


826 


.7277 


585 


59 


2 


249 


.24995 


4.0009 


015 


58 


2 


938 


857 


.7234 


578 


58 


3 


277 


.25026 


3.9959 


008 


57 


3 


966 


888 


.7191 


570 


57 


4 


305 


056 


.9910' 


.97001 


56 


4 


.25994 


920 


.7148 


562 


56 


5 


.24333 


.25087 


3.9861 


.96994 


55 


5 


.26022 


.26951 


3.7105 


.96555 


55 


6 


362 


118 


.9812 


987 


54 


6 


050 


.26982 


.7062 


547 


54 


7 


390 


149 


.9763 


980 


53 


7 


079 


.27013 


.7019 


540 


53 


8 


418 


180 


.9714 


973 


52 


8 


107 


044 


.6976 


532 


52 


9 


446 


211 


.9665 


966 


51 


9 


135 


076 


.6933 


524 


51 


10 


.24474 


.25242 


3.9617 


.96959 


50 


10 


.26163 


.27107 


3.6891 


.96517 


50 


11 


503 


273 


.9568 


952 


49 


11 


191 


138 


.6848 


509 


49 


12 


531 


304 


.9520 


945 


48 


12 


219 


169 


.6806 


502 


48 


13 


559 


335 


.9471 


937 


47 


13 


247 


201 


.6764 


494 


47 


14 


587 


366 


.9423 


930 


46 


14 


275 


232 


.6722 


486 


46 


15 


.24615 


.25397 


3.9375 


.96923 


45 


15 


.26303 


.27263 


3.6680 


.96479 


45 


16 


644 


428 


.9327 


916 


44 


16 


331 


294 


.6638 


471 


44 


17 


672 


459 


.9279 


909 


43 


17 


359 


326 


.6596 


463 


43 


18 


700 


490 


.9232 


902 


42 


18 


387 


357 


.6554 


456 


42 


19 


728 


521 


.9184 


894 


41 


19 


415 


388 


.6512 


448 


41 


20 


.24756 


.25552 


3.9136 


.96887 


40 


20 


.26443 


.27419 


3.6470 


.96440 


40 


21 


784 


583 


.9089 


880 


39 


21 


471 


451 


.6429 


433 


39 


22 


813 


614 


.9042 


873 


38 


22 


500 


482 


.6387 


425 


38 


23 


841 


645 


.8995 


866 


37 


23 


528 


513 


.6346 


417 


37 


24 


869 


676 


.8947 


858 


36 


24 


556 


545 


.6305 


410 


36 


25 


.24897 


.25707 


3.8900 


.96851 


35 


25 


.26584 


.27576 


3.6264 


.96402 


35 


26 


925 


738 


.8854 


844 


34 


26 


612 


607 


.6222 


394 


34 


27 


954 


769 


.8807 


837 


33 


27 


640 


638 


.6181 


386 


33 


28 


.24982 


800 


.8760 


829 


32 


28 


668 


670 


.6140 


379 


32 


29 


.25010 


831 


.8714 


822 


31 


29 


696 


701 


.6100 


371 


31 


30 


.25038 


.25862 


3.8667 


.96815 


30 


30 


.26724 


.27732 


3.6059 


.96363 


30 


31 


066 


893 


.8621 


807 


29 


31 


752 


764 


.6018 


355 


29 


32 


094 


924 


.8575 


800 


28 


32 


780 


795 


.5978 


347 


28 


33 


122 


955 


.8528 


793 


27 


33 


808 


826 


.5937 


340 


27 


34 


151 


.25986 


.8482 


786 


26 


34 


836 


858 


.5897 


332 


26 


35 


.25179 


.26017 


3.8436 


.96778 


25 


35 


.26864 


.27889 


3.5856 


.96324 


25 


36 


207 


048 


.8391 


771 


24 


36 


892 


921 


.5816 


316 


24 


37 


235 


079 


.8345 


764 


23 


37 


920 


952 


.5776 


308 


23 


38 


263 


110 


.8299 


756 


22 


38 


948 


.27983 


.5736 


301 


22 


39 


291 


141 


.8254 


749 


21 


39 


.26976 


.28015 


.5696 


293 


21 


40 


.25320 


.26172 


3.8208 


.96742 


20 


40 


.27004 


.28046 


3.5656 


.96285 


20 


41 


348 


203 


.8163 


734 


19 


41 


032 


077 


.5616 


277 


19 


42 


376 


235 


.8118 


727 


18 


42 


060 


109 


.5576 


269 


18 


43 


404 


266 


.8073 


719 


17 


43 


088 


140 


.5536 


261 


17 


44 


432 


297 


.8028 


712 


16 


44 


116 


172 


.5497 


253 


16 


45 


.25460 


.26328 


3.7983 


.96705 


15 


45 


.27144 


.28203 


3.5457 


.96246 


15 


46 


488 


359 


.7938 


697 


14 


46 


172 


234 


.5418 


238 


14 


47 


516 


390 


.7893 


690 


13 


47 


200 


266 


.5379 


230 


13 


48 


545 


421 


.7848 


682 


12 


48 


228 


297 


.5339 


222 


12 


49 


573 


452 


.7804 


675 


11 


49 


256 


329 


.5300 


214 


11 


50 


.25601 


.26483 


3.7760 


.96667 


10 


50 


.27284 


.28360 


3.5261 


.96206 


10 


51 


629 


515 


.7715 


660 


9 


51 


312 


391 


.5222 


198 


9 


52 


657 


546 


.7671 


653 


8 


52 


340 


423 


.5183 


190 


8 


53 


685 


577 


.7627 


645 


7 


53 


368 


454 


.5144 


182 


7 


54 


713 


608 


.7583 


638 


6 


54 


396 


486 


.5105 


174 


6 


55 


.25741 


.26639 


3.7539 


.96630 


5 


55 


.27424 


.28517 


3.5067 


.96166 


5 


56 


769 


670 


.7495 


623 


4 


56 


452 


549 


.5028 


158 


4 


57 


798 


701 


.7451 


615 


3 


57 


480 


580 


.4989 


150 


3 


58 


826 


733 


.7408 


608 


2 


58 


508 


612 


.4951 


142 


2 


59 


854 


764 


.7364 


600 


1 


59 


536 


643 


.4912 


134 


1 


60 


.25882 


.26795 


3.7321 


.96593 


° 


60 


.27564 


.28675 


3.4874 


.96126 







Cos 


Ctn 


Tan 


Sin 


1 




Cos 


Ctn 


Tan 


Sin 


/ 



75° 



74° 



30 


16° — Values of Trigonometric Functions — 17° 


[II 


/ 


Sin 


Tan 


Ctn 


Cos 




/ 


Sin 


Tan 


Ctn 


Cos 







.27564 


.28675 


3.4874 


.96126 


60 





.29237 


.30573 


3.2709 


.95630 


60 


1 


592 


706 


.4836 


118 


59 


1 


265 


605 


.2675 


622 


59 


2 


620 


738 


.4798 


110 


58 


2 


293 


637 


.2641 


613 


58 


3 


648 


769 


.4760 


102 


57 


3 


321 


669 


.2607 


605 


57 


4 


676 


801 


.4722 


094 


56 


4 


348 


700 


.2573 


596 


56 


5 


.27704 


.28832 


3.4684 


.96086 


55 


5 


.29376 


.30732 


3.2539 


.95588 


55 


6 


731 


864 


.4646 


078 


54 


i 6 


404 


764 


.2506 


579 


54 


7 


759 


895 


.4608 


070 


53 


7 


432 


796 


.2472 


571 


53 


8 


787 


927 


.4570 


062 


52 


8 


460 


828 


.2438 


562 


52 


9 


815 


958 


.4533 


054 


51 


9 


487 


860 


.2405 


554 


51 


10 


.27843 


.28990 


3.4495 


.96046 


50 


10 


.29515 


.30891 


3.2371 


.95545 


50 


11 


871 


.29021 


.4458 


037 


49 


11 


543 


923 


.2338 


536 


49 


12 


899 


053 


.4420 


029 


48 


12 


571 


955 


.2305 


528 


48 


13 


927 


084 


.4383 


021 


47 


13 


599 


.30987 


.2272 


519 


47 


14 


955 


116 


.4346 


013 


46 


14 


626 


.31019 


.2238 


511 


46 


15 


.27983 


.29147 


3.4308 


.96005 


45 


15 


.29654 


.31051 


3.2205 


.95502 


45 


16 


.28011 


179 


.4271 


.95997 


44 


16 


682 


083 


.2172 


493 


44 


17 


039 


210 


.4234 


989 


43 


17 


710 


115 


.2139 


485 


43 


18 


067 


242 


.4197 


981 


42 


18 


737 


147 


.2106 


476 


42 


19 


095 


274 


.4160 


972 


41 


19 


765 


178 


.2073 


467 


41 


20 


.28123 


.29305 


3.4124 


.95964 


40 


20 


.29793 


.31210 


3.2041 


.95459 


40 


21 


150 


337 


.4087 


956 


39 


21 


821 


242 


.2008 


450 


39 


22 


178 


368 


.4050 


948 


38 


22 


849 


274 


.1975 


441 


38 


23 


206 


400 


.4014 


940 


37 


23 


876 


306 


.1943 


433 


37 


24 


234 


432 


.3977 


931 


36 


24 


904 


338 


.1910 


424 


36 


25 


.28262 


.29463 


3.3941 


.95923 


35 


25 


.29932 


.31370 


3.1878 


.95415 


35 


26 


290 


495 


.3904 


915 


34 


26 


960 


402 


.1845 


407 


34 


27 


318 


526 


.3868 


907 


33 


27 


.29987 


434 


.1813 


398 


33 


28 


346 


558 


.3832 


898 


32 


28 


.30015 


466 


.1780 


389 


32 


29 


374 


590 


.3796 


890 


31 


29 


043 


498 


.1748 


380 


31 


30 


.28402 


.29621 


3.3759 


.95882 


30 


30 


.30071 


.31530 


3.1716 


.95372 


30 


31 


429 


653 


.3723 


874 


29 


31 


098 


562 


.1684 


363 


29 


32 


457 


685 


.3687 


865 


28 


32 


126 


594 


.1652 


354 


28 


33 


485 


716 


.3652 


857 


27 


33 


154 


626 


.1620 


345 


27 


34 


513 


748 


.3616 


849 


26 


34 


182 


658 


.1588 


337 


26 


35 


.28541 


.29780 


3.3580 


.95841 


25 


35 


.30209 


.31690 


3.1556 


.95328 


25 


36 


569 


811 


.3544 


832 


24 


36 


237 


722 


.1524 


319 


24 


37 


597 


843 


.3509 


824 


23 


37 


265 


754 


.1492 


310 


23 


38 


625 


875 


.3473 


816 


22 


38 


292 


786 


.1460 


301 


22 


39 


652 


906 


.3438 


807 


21 


39 


320 


818 


.1429 


293 


21 


40 


.28680 


.29938 


3.3402 


.95799 


20 


40 


.30348 


.31850 


3.1397 


.95284 


20 


41 


708 


.29970 


.3367 


791 


19 


41 


376 


882 


.1366 


275 


19 


42 


736 


.30001 


.3332 


782 


18 


42 


403 


914 


.1334 


266 


18 


43 


764 


033 


.3297 


774 


17 


43 


431 


946 


.1303 


257 


17 


44 


792 


065 


.3261 


766 


16 


44 


459 


.31978 


.1271 


248 


16 


45 


.28820 


.30097 


3.3226 


.95757 


15 


45 


.30486 


.32010 


3.1240 


.95240 


15 


46 


847 


128 


.3191 


749 


14 


46 


514 


042 


.1209 


231 


14 


47 


875 


160 


.3156 


740 


13 


47 


542 


074 


.1178 


222 


13 


48 


903 


192 


.3122 


732 


12 


48 


570 


106 


.1146 


213 


12 


49 


931 


224 


.3087 


724 


11 


49 


597 


139 


.1115 


204 


11 


50 


.28959 


.30255 


3.3052 


.95715 


10 


50 


.30625 


.32171 


3.1084 


.95195 


10 


51 


.28987 


287 


.3017 


707 


9 


51 


653 


203 


.1053 


186 


9 


52 


.29015 


319 


.2983 


698 


8 


52 


680 


235 


.1022 


177 


8 


53 


042 


351 


.2948 


690 


7 


53 


708 


267 


.0991 


168 


7 


54 


070 


382 


.2914 


681 


6 


54 


736 


299 


.0961 


159 


6 


55 


.29098 


.30414 


3.2879 


.95673 


5 


55 


.30763 


.32331 


3.0930 


.95150 


5 


56 


126 


446 


.2845 


664 


4 


56 


791 


363 


.0899 


142 


4 


57 


154 


478 


.2811 


656 


3 


57 


819 


396 


.0868 


133 


3 


58 


182 


509 


.2777 


647 


2 


58 


846 


428 


.0838 


124 


2 


59 


209 


541 


.2743 


639 


1 


59 


874 


460 


.0807 


115 


1 


60 


.29237 


.30573 


3.2709 


.95630 





60 


.30902 


.32492 


3.0777 


.95106 







Cos 


Ctn 


Tan 


Sin 


/ 




Cos 


Ctn 


Tan 


Sin J 


/ 



73° 



72' 



II] 


18° — Values of Trigonometric Functions — 19° 


31 


/ 


Sin 


Tan 


Ctn 


Cos 




/ 


Sin 


Tan 


Ctn 


Cos 







.30902 


.32492 


3.0777 


.95106 


60 





.32557 


.34433 


2.9042 


.94552 


60 


1 


929 


524 


.0746 


097 


59 


1 


584 


465 


.9015 


542 


59 


2 


957 


556 


.0716 


088 


58 


2 


612 


498 


.8987 


533 


58 


3 


.30985 


588 


.0686 


079 


57 


3 


639 


530 


.8960 


523 


57 


4 


.31012 


621 


.0655 


070 


56 


4 


667 


563 


.8933 


514 


56 


5 


.31040 


.32653 


3.0625 


.95061 


55 


5 


.32694 


.34596 


2.8905 


.94504 


55 


6 


068 


685 


.0595 


052 


54 


6 


722 


628 


.8878 


495 


54 


7 


095 


717 


.0565 


043 


53 


7 


749 


661 


.8851 


485 


53 


8 


123 


749 


.0535 


033 


52 


8 


777 


693 


.8824 


476 


52 


9 


151 


782 


.0505 


024 


51 


9 


804 


726 


.8797 


466 


51 


10 


.31178 


.32814 


3.0475 


.95015 


50 


10 


.32832 


.34758 


2.8770 


.94457 


50 


11 


206 


846 


.0445 


.95006 


49 


11 


859 


791 


.8743 


447 


49 


12 


233 


878 


.0415 


.94997 


48 


12 


887 


824 


.8716 


438 


48 


13 


261 


911 


.0385 


988 


47 


13 


914 


856 


.8689 


428 


47 


14 


289 


943 


.0356 


979 


46 


14 


942 


889 


.8662 


418 


46 


15 


.31316 


.32975 


3.0326 


.94970 


45 


15 


.32969 


.34922 


2.8636 


.94409 


45 


16 


344 


.33007 


.0296 


961 


44 


16 


.32997 


954 


.8609 


399 


44 


17 


372 


040 


.0267 


952 


43 


17 


.33024 


.34987 


.8582 


390 


43 


18 


399 


072 


.0237 


943 


42 


18 


051 


.35020 


.8556 


380 


42 


19 


427 


104 


.0208 


933 


41 


19 


079 


052 


.8529 


370 


41 


20 


.31454 


.33136 


3.0178 


.94924 


40 


20 


.33106 


.35085 


2.8502 


.94361 


40 


21 


482 


169 


.0149 


915 


39 


21 


134 


118 


.8476 


351 


39 


22 


510 


201 


.0120 


906 


38 


22 


161 


150 


.8449 


342 


38 


23 


537 


233 


.0090 


897 


37 


23 


189 


183 


.8423 


332 


37 


24 


565 


266 


.0061 


888 


36 


24 


216 


216 


.8397 


322 


36 


25 


.31593 


.33298 


3.0032 


.94878 


35 


25 


.33244 


.35248 


2.8370 


.94313 


35 


26 


620 


330 


3.0003 


869 


34 


26 


271 


281 


.8344 


303 


34 


27 


648 


363 


2.9974 


860 


33 


27 


298 


314 


.8318 


293 


33 


28 


675 


395 


.9945 


851 


32 


28 


326 


346 


.8291 


284 


32 


29 


703 


427 


.9916 


842 


31 


29 


353 


379 


.8265 


274 


31 


30 


.31730 


.33460 


2.9887 


.94832 


30 


30 


.33381 


.35412 


2.8239 


.94264 


30 


31 


758 


492 


.9858 


823 


29 


31 


408 


445 


.8213 


254 


29 


32 


786 


524 


.9829 


814 


28 


32 


436 


477 


.8187 


245 


28 


33 


813 


557 


.9800 


805 


27 


33 


463 


510 


.8161 


235 


27 


34 


841 


589 


.9772 


795 


26 


34 


490 


543 


.8135 


225 


26 


35 


.31868 


.33621 


2.9743 


.94786 


25 


35 


.33518 


.35576 


2.8109 


.94215 


25 


36 


896 


654 


.9714 


777 


24 


36 


545 


608 


.8083 


206 


24 


37 


923 


686 


.9686 


768 


23 


37 


573 


641 


.8057 


196 


23 


38 


951 


718 


.9657 


758 


22 


38 


600 


674 


.8032 


186 


22 


39 


.31979 


751 


.9629 


749 


21 


39 


627 


707 


.8006 


176 


21 


40 


.32006 


.33783 


2.9600 


.94740 


20 


40 


.33655 


.35740 


2.7980 


.94167 


20 


41 


034 


816 


.9572 


730 


19 


41 


682 


772 


.7955 


157 


19 


42 


061 


848 


.9544 


721 


18 


42 


710 


805 


.7929 


147 


18 


43 


089 


881 


.9515 


712 


17 


43 


737 


838 


.7903 


137 


17 


44 


116 


913 


.9487 


702 


16 


44 


764 


871 


.7878 


127 


16 


45 


.32144 


.33945 


2.9459 


.94693 


15 


45 


.33792 


.35904 


2.7852 


.94118 


15 


46 


171 


.33978 


.9431 


684 


14 


46 


819 


937 


.7827 


108 


14 


47 


199 


.34010 


.9403 


674 


13 


47 


846 


.35969 


.7801 


098 


13 


48 


227 


043 


.9375 


665 


12 


48 


874 


.36002 


.7776 


088 


12 


49 


254 


075 


.9347 


656 


11 


49 


901 


035 


.7751 


078 


11 


50 


.32282 


.34108 


2.9319 


.94646 


10 


50 


.33929 


.36068 


2.7725 


.94068 


10 


51 


309 


140 


.9291 


637 


9 


51 


956 


101 


.7700 


058 


9 


52 


337 


173 


.9263 


627 


8 


52 


.33983 


134 


.7675 


049 


8 


53 


364 


205 


.9235 


618' 


7 


53 


.34011 


167 


.7650 


039 


7 


54 


392 


238 


.9208 


609 


6 


54 


038 


199 


.7625 


029 


6 


55 


.32419 


.34270 


2.9180 


.94599 


5 


55 


.34065 


.36232 


2.7600 


.94019 


5 


56 


447 


303 


.9152 


590 


4 


56 


093 


265 


.7575 


.94009 


4 


57 


474 


335 


.9125 


580 


3 


57 


120 


298 


.7550 


.93999 


3 


58 


502 


368 


.9097 


571 


2 


58 


147 


331 


.7525 


989 


2 


59 


529 


400 


.9070 


561 


1 


59 


175 


364 


.7500 


979 


1 


60 


.32557 


.34433 


2.9042 


.94552 





60 


.34202 


.36397 


2.7475 


.93969 







1 Cos 


Ctn | Tan 


Sin 


/ 




Cos 


Ctn 


Tan 


Sin 





71' 



70' 



32 



20° — Values of Trigonometric Functions — 21 



PI 



/ 


Sin 


Tan 


Ctn 


Cos 







.34202 


.36397 


2.7475 


.93969 


60 


1 


229 


430 


.7450 


959 


59 


2 


257 


463 


.7425 


949 


58 


3 


284 


496 


.7400 


939 


57 


4 


311 


529 


.7376 


929 


56 


5 


.34339 


.36562 


2.7351 


.93919 


55 


6 


366 


595 


.7326 


909 


54 


7 


393 


628 


.7302 


899 


53 


8 


421 


661 


.7277 


889 


52 


9 


448 


694 


.7253 


879 


51 


10 


.34475 


.36727 


2.7228 


.93869 


50 


11 


503 


760 


.7204 


859 


49 


12 


530 


793 


.7179 


849 


48 


13 


557 


826 


.7155 


839 


47 


14 


584 


859 


.7130 


829 


46 


15 


.34612 


.36892 


2.7106 


.93819 


45 


16 


639 


925 


.7082 


809 


44 


17 


666 


958 


.7058 


799 


43 


18 


694 


.36991 


.7034 


789 


42 


19 


721 


.37024 


.7009 


779 


41 


20 


.34748 


.37057 


2.6985 


.93769 


40 


21 


775 


090 


.6961 


759 


39 


22 


803 


123 


.6937 


748 


38 


23 


830 


157 


.6913 


738 


37 


24 


857 


190 


.6889 


728 


36 


25 


.34884 


.37223 


2.6865 


.93718 


35 


26 


912 


256 


.6841 


708 


34 


27 


939 


289 


.6818 


698 


33 


28 


966 


322 


.6794 


688 


32 


29 


.34993 


355 


.6770 


677 


31 


30 


.35021 


.37388 


2.6746 


.93667 


30 


31 


048 


422 


.6723 


657 


29 


32 


075 


455 


.6699 


647 


28 


33 


102 


488 


.6675 


637 


27 


34 


130 


521 


.6652 


626 


26 


35 


.35157 


.37554 


2.6628 


.93616 


25 


36 


184 


588 


.6605 


606 


24 


37 


211 


621 


.6581 


596 


23 


38 


239 


654 


.6558 


585 


22 


39 


266 


687 


.6534 


575 


21 


40 


.35293 


.37720 


2.6511 


.93565 


20 


41 


320 


754 


.6488 


555 


19 


42 


347 


787 


.6464 


544 


18 


43 


375 


820 


.6441 


534 


17 


44 


402 


853 


.6418 


524 


16 


45 


.35429 


.37887 


2.6395 


.93514 


15 


46 


456 


920 


.6371 


503 


14 


47 


484 


953 


.6348 


493 


13 


48 


511 


.37986 


.6325 


483 


12 


49 


538 


.38020 


.6302 


472 


11 


50 


.35565 


.38053 


2.6279 


.93462 


10 


51 


592 


086 


.6256 


452 


9 


52 


619 


120 


.6233 


441 


8 


53 


647 


153 


.6210 


431 


7 


54 


674 


186 


.6187 


420 


6 


55 


.35701 


.38220 


2.6165 


.93410 


5 


56 


728 


253 


.6142 


400 


4 


57 


755 


286 


.6119 


389 


3 


58 


782 


320 


.6096 


379 


2 


59 


810 


353 


.6074 


368 


1 


60 


.35837 


.38386 


2.6051 


.93358 


C 




Cos 


Ctn 


Tan 


Sin 


/ 



/ 


Sin 


Tan 


Ctn 


Cos 







.35837 


.38386 


2.6051 


.93358 


60 


1 


864 


420 


.6028 


348 


59 


2 


891 


453 


.6006 


337 


58 


3 


918 


487 


.5983 


327 


57 


4 


945 


520 


.5961 


316 


56 


5 


.35973 


.38553 


2.5938 


.93306 


55 


6 


.36000 


587 


.5916 


295 


54 


7 


027 


620 


.5893 


285 


53 


8 


054 


654 


.5871 


274 


52 


9 


081 


687 


.5848 


264 


51 


10 


.36108 


.38721 


2.5826 


.93253 


50 


11 


135 


754 


.5804 


243 


49 


12 


162 


787 


.5782 


232 


48 


13 


190 


821 


.5759 


222 


47 


14 


217 


854 


.5737 


211 


46 


15 


.36244 


.38888 


2.5715 


.93201 


45 


16 


271 


921 


.5693 


190 


44 


17 


298 


955 


.5671 


180 


43 


18 


325 


.38988 


.5649 


169 


42 


19 


352 


.39022 


.5627 


159 


41 


20 


.36379 


.39055 


2.5605 


.93148 


40 


21 


406 


089 


.5583 


137 


39 


22 


434 


122 


.5561 


127 


38 


23 


461 


156 


.5539 


116 


37 


24 


488 


190 


.5517 


106 


36 


25 


.36515 


.39223 


2.5495 


.93095 


35 


26 


542 


257 


.5473 


084 


34 


27 


569 


290 


.5452 


074 


33 


28 


596 


324 


.5430 


063 


32 


29 


623 


357 


.5408 


052 


31 


30 


.36650 


.39391 


2.5386 


.93042 


30 


31 


677 


425 


.5365 


031 


29 


32 


704 


458 


.5343 


020 


28 


33 


731 


492 


.5322 


.93010 


27 


34 


758 


526 


.5300 


.92999 


26 


35 


.36785 


.39559 


2.5279 


.92988 


25 


36 


812 


593 


.5257 


978 


24 


37 


839 


626 


.5236 


967 


23 


38 


867 


660 


.5214 


956 


22 


39 


894 


694 


.5193 


945 


21 


40 


.36921 


.39727 


2.5172 


.92935 


20 


41 


948 


761 


.5150 


924 


19 


42 


.36975 


795 


.5129 


913 


18 


43 


.37002 


829 


.5108 


902 


17 


44 


029 


862 


.5086 


892 


16 


45 


.37056 


.39896 


2.5065 


.92881 


15 


46 


083 


930 


.5044 


870 


14 


47 


110 


963 


.5023 


859 


13 


48 


137 


.39997 


.5002 


849 


12 


49 


164 


.40031 


.4981 


838 


11 


50 


.37191 


.40065 


2.4960 


.92827 


10 


51 


218 


098 


.4939 


816 


9 


52 


245 


132 


.4918 


805 


8 


53 


272 


166 


.4897 


794 


7 


54 


299 


200 


.4876 


784 


6 


55 


.37326 


.40234 


2.4855 


.92773 


5 


56 


353 


267 


.4834 


762 


4 


57 


380 


301 


.4813 


751 


3 


58 


407 


335 


.4792 


740 


2 


59 


434 


369 


.4772 


729 


1 


60 


.37461 


.40403 


2.4751 


.92718 







Cos 


Ctn 


Tan 


Sin 



69' 



68° 



II] 22° — Values of Trigonometric Functions — 23' 



33 



/ 


Sin 


Tan 


Ctn 


Cos 







.37461 


.40403 


2.4751 


.92718 


60 


1 


488 


436 


.4730 


707 


59 


2 


515 


470 


.4709 


697 


58 


3 


542 


504 


.4689 


686 


57 


4 


569 


538 


.4668 


675 


56 


5 


.37595 


.40572 


2.4648 


.92664 


55 


6 


622 


606 


.4627 


653 


54 


7 


649 


640 


.4606 


642 


53 


8 


676 


674 


.4586 


631 


52 


9 


703 


707 


.4566 


620 


51 


10 


.37730 


.40741 


2.4545 


.92609 


50 


11 


757 


775 


.4525 


598 


49 


12 


784 


809 


.4504 


587 


48 


13 


811 


843 


.4484 


576 


47 


14 


838 


877 


.4464 


565 


46 


15 


.37865 


.40911 


2.4443 


.92554 


45 


16 


892 


945 


.4423 


543 


44 


17 


919 


.40979 


.4403 


532 


43 


18 


946 


.41013 


.4383 


521 


42 


19 


973 


047 


.4362 


510 


41 


20 


.37999 


.41081 


2.4342 


.92499 


40 


21 


.38026 


115 


.4322 


488 


39 


22 


053 


149 


.4302 


477 


38 


23 


080 


183 


.4282 


466 


37 


24 


107 


217 


.4262 


455 


36 


25 


.38134 


.41251 


2.4242 


.92444 


35 


26 


161 


285 


.4222 


432 


34 


27 


188 


319 


.4202 


421 


33 


28 


215 


353 


.4182 


410 


32 


29 


241 


387 


.4162 


399 


31 


30 


.38268 


.41421 


2.4142 


.92388 


30 


31 


295 


455 


.4122 


377 


29 


32 


322 


490 


.4102 


366 


28 


33 


349 


524 


.4083 


355 


27 


34 


376 


558 


.4063 


343 


26 


35 


.38403 


.41592 


2.4043 


.92332 


25 


36 


430 


626 


.4023 


321 


24 


37 


456 


660 


.4004 


310 


23 


38 


483 


694 


.3984 


299 


22 


39 


510 


728 


.3964 


287 


21 


40 


.38537 


.41763 


2.3945 


.92276 


20 


41 


564 


797 


.3925 


265 


19 


42 


591 


831 


.3906 


254 


18 


43 


617 


865 


.3886 


243 


17 


44 


644 


899 


.3867 


231 


16 


45 


.38671 


.41933 


2.3847 


.92220 


15 


46 


698 


.41968 


.3828 


209 


14 


47 


725 


.42002 


.3808 


198 


13 


48 


752 


036 


.3789 


186 


12 


49 


778 


070 


.3770 


175 


11 


50 


.38805 


.42105 


2.3750 


.92164 


10 


51 


832 


139 


.3731 


152 


9 


52 


859 


173 


.3712 


141 


8 


53 


886 


207 


.3693 


130 


7 


54 


912 


242 


.3673 


119 


6 


55 


.38939 


.42276 


2.3654 


.92107 


5 


56 


966 


310 


.3635 


096 


4 


57 


.38993 


345 


.3616 


085 


3 


58 


.39020 


379 


.3597 


073 


2 


59 


046 


413 


.3578 


062 


1 


60 


.39073 


.42447 


2.3559 


.92050 







Cos 


Ctn 


Tan 


Sin 


/ 



/ 


Sin 


Tan 


Ctn 


Cos 







.39073 


.42447 


2.3559 


.92050 


60 


1 


100 


482 


.3539 


039 


59 


2 


127 


516 


.3520 


028 


58 


3 


153 


551 


.3501 


016 


57 


4 


180 


585 


.3483 


.92005 


56 


5 


.39207 


.42619 


2.3464 


.91994 


55 


6 


234 


654 


.3445 


982 


54 


7 


260 


688 


.3426 


971 


53 


8 


287 


722 


.3407 


959 


52 


9 


314 


757 


.3388 


948 


51 


10 


.39341 


.42791 


2.3369 


.91936 


50 


11 


367 


826 


.3351 


925 


49 


12 


394 


860 


.3332 


914 


48 


13 


421 


894 


.3313 


902 


47 


14 


448 


929 


.3294 


891 


46 


15 


.39474 


.42963 


2.3276 


.91879 


45 


16 


501 


.42998 


.3257 


868 


44 


17 


528 


.43032 


.3238 


856 


43 


18 


555 


067 


.3220 


845 


42 


19 


581 


101 


.3201 


833 


41 


20 


.39608 


.43136 


2.3183 


.91822 


40 


21 


635 


170 


.3164 


810 


39 


22 


661 


205 


.3146 


799 


38 


23 


688 


239 


.3127 


787 


37 


24 


715 


274 


.3109 


775 


36 


25 


.39741 


.43308 


2.3090 


.91764 


35 


26 


768 


343 


.3072 


752 


34 


27 


795 


378 


.3053 


741 


33 


28 


822 


412 


.3035 


729 


32 


29 


848 


447 


.3017 


718 


31 


30 


.39875 


.43481 


2.2998 


.91706 


30 


31 


902 


516 


.2980 


694 


29 


32 


928 


550 


.2962 


683 


28 


33 


955 


585 


.2944 


671 


27 


34 


.39982 


620 


.2925 


660 


26 


35 


.40008 


.43654 


2.2907 


.91648 


25 


36 


035 


689 


.2889 


636 


24 


37 


062 


724 


.2871 


625 


23 


38 


088 


758 


.2853 


613 


22 


39 


115 


793 


.2835 


601 


21 


40 


.40141 


.43828 


2.2817 


.91590 


20 


41 


168 


862 


.2799 


578 


19 


42 


195 


897 


.2781 


566 


18 


43 


221 


932 


.2763 


555 


17 


44 


248 


.43966 


.2745 


543 


16 


45 


.40275 


.44001 


2.2727 


.91531 


15 


46 


301 


036 


.2709 


519 


14 


47 


328 


071 


.2691 


508 


13 


48 


355 


105 


.2673 


496 


12 


49 


381 


140 


.2655 


484 


11 


50 


.40408 


.44175 


2.2637 


.91472 


10 


51 


434 


210 


.2620 


461 


9 


52 


461 


244 


.2602 


449 


8 


53 


488 


279 


.2584 


437 


7 


54 


514 


314 


.2566 


425 


6 


55 


.40541 


.44349 


2.2549 


.91414 


5 


56 


567 


384 


.2531 


402 


4 


57 


594 


418 


.2513 


390 


3 


58 


621 


453 


.2496 


378 


2 


59 


647 


488 


.2478 


366 


1 


60 


.40674 


.44523 


2.2460 


.91355 





1 


Cos 


Ctn 


Tan 


Sin 


/ 



67< 



66° 



34 



24° — Values of Trigonometric Functions — 25 c 



[II 



o 

i 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 

12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



Sin Tan Ctn Cos 



.40674 
700 
727 
753 
780 

.40806 
833 
860 
886 
913 

.40939 
966 

.40992 

.41019 
045 

.41072 
098 
125 
151 
178 

.41204 
231 
257 
284 
310 

.41337 
363 
390 
416 
443 

.41469 
496 
522 
549 
575 

.41602 
628 
655 
681 
707 

.41734 
760 
787 
813 
840 

.41866 
892 
919 
945 
972 

.41998 

.42024 

051 

077 

104 

.42130 
156 
183 
209 
235 

.42262 



.44523 
558 
593 
627 
662 

.44697 
732 
767 
802 
837 

.44872 

907 

942 

.44977 

.45012 

.45047 
082 
117 
152 
187 

.45222 
257 
292 
327 
362 

.45397 
432 
467 
502 
538 

.45573 

608 
643 
678 
713 

.45748 
784 
819 
854 
889 

.45924 
960 

.45995 

.46030 
065 

.46101 
136 
171 
206 
242 

.46277 
312 
348 
383 

418 

.46454 
489 
525 
560 
595 

.46631 



2.2460 
.2443 
.2425 
.2408 
.2390 

2.2373 
.2355 
.2338 
.2320 
.2303 

2.2286 
.2268 
.2251 
.2234 
.2216 

2.2199 
.2182 
.2165 
.2148 
.2130 

2.2113 

.2096 
.2079 
.2062 
.2045 
2.2028 
.2011 
.1994 
.1977 
.1960 

2.1943 
.1926 
.1909 
.1892 
.1876 

2.1859 
.1842 
.1825 
.1808 
.1792 

2.1775 
.1758 
.1742 
.1725 
.1708 

2.1692 
.1675 
.1659 
.1642 
.1625 

2.1609 
.1592 
.1576 
.1560 
.1543 

2.1527 
.1510 
.1494 

.1478 
.1461 

2.1445 



.91355 
343 
331 
319 
307 

.91295 
283 
272 

260 

248 

.91236 
224 
212 

200 

188 

.91176 
164 
152 
140 
128 

.91116 
104 
092 
080 
068 

.91056 
044 
032 
020 

.91008 

.90996 
984 
972 
960 

948 

.90936 
924 
911 

899 

887 

.90875 
863 
851 
839 
826 

.90814 
802 
790 

778 
766 

.90753 
741 
729 
717 

704 

.90692 
680 
668 
655 
643 

.90631 



Cos Ctn Tan Sin 

~ ~ ~ 65° 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




/ 


Sin 


Tan 


Ctn 


Cos 







.42262 


.46631 


2.1445 


.90631 


60 


1 


288 


666 


.1429 


618 


59 


2 


315 


702 


.1413 


606 


58 


3 


341 


737 


.1396 


594 


57 


4 


367 


772 


.1380 


582 


56 


5 


.42394 


.46808 


2.1364 


.90569 


55 


6 


420 


843 


.1348 


557 


54 


7 


446 


879 


.1332 


545 


53 


8 


473 


914 


.1315 


532 


52 


9 


499 


950 


.1299 


520 


51 


10 


.42525 


.46985 


2.1283 


.90507 


50 


11 


552 


.47021 


.1267 


495 


49 


12 


578 


056 


.1251 


483 


48 


13 


604 


092 


.1235 


470 


47 


14 


631 


128 


.1219 


458 


46 


15 


.42657 


.47163 


2.1203 


.90446 


45 


16 


683 


199 


.1187 


433 


44 


17 


709 


234 


.1171 


421 


43 


18 


736 


270 


.1155 


408 


42 


19 


762 


305 


.1139 


396 


41 


20 


.42788 


.47341 


2.1123 


.90383 


40 


21 


815 


377 


.1107 


371 


39 


22 


841 


412 


.1092 


358 


38 


23 


867 


448 


.1076 


346 


37 


24 


894 


483 


.1060 


334 


36 


25 


.42920 


.47519 


2.1044 


.90321 


35 


26 


946 


555 


.1028 


309 


34 


27 


972 


590 


.1013 


296 


33 


28 


.42999 


626 


.0997 


284 


32 


29 


.43025 


662 


.0981 


271 


31 


30 


.43051 


.47698 


2.0965 


.90259 


30 


31 


077 


733 


.0950 


246 


29 


32 


104 


769 


.0934 


233 


28 


33 


130 


805 


.0918 


221 


27 


34 


156 


840 


.0903 


208 


26 


35 


.43182 


.47876 


2.0887 


.90196 


25 


36 


209 


912 


.0872 


183 


24 


37 


235 


948 


.0856 


171 


23 


38 


261 


.47984 


.0840 


158 


22 


39 


287 


.48019 


.0825 


146 


21 


40 


.43313 


.48055 


2.0809 


.90133 


20 


41 


340 


091 


.0794 


120 


19 


42 


366 


127 


.0778 


108 


18 


43 


392 


163 


.0763 


095 


17 


44 


418 


198 


.0748 


082 


16 


45 


.43445 


.48234 


2.0732 


.90070 


15 


46 


471 


270 


.0717 


057 


14 


47 


497 


306 


.0701 


045 


13 


48 


523 


342 


.0686 


032 


12 


49 


549 


378 


.0671 


019 


11 


50 


.43575 


.48414 


2.0655 


.90007 


10 


51 


602 


450 


.0640 


.89994 


9 


52 


628 


486 


.0625 


981 


8 


53 


654 


521 


.0609 


968 


7 


54 


680 


557 


.0594 


956 


6 


55 


.43706 


.48593 


2.0579 


.89943 


5 


56 


733 


629 


.0564 


930 


4 


57 


759 


665 


.0549 


918 


3 


58 


785 


701 


.0533 


905 


2 


59 


811 


737 


.0518 


892 


1 


60 


.43837 


.48773 


2.0503 


.89879 







1 Cos 


Ctn 


Tan 


Sin 


/ 



64< 



II] 26° — Values of Trigonometric Functions — 27' 



35 



/ 


Sin 


Tan 


Ctn 


Cos 







.43837 


.48773 


2.0503 


.89879 


60 


1 


863 


809 


.0488 


867 


59 


2 


889 


845 


.0473 


854 


58 


3 


916 


881 


.0458 


841 


57 


4 


942 


917 


.0443 


828 


56 


5 


.43968 


.48953 


2.0428 


.89816 


55 


6 


.43994 


.48989 


.0413 


803 


54 


7 


.44020 


.49026 


.0398 


790 


53 


8 


046 


062 


.0383 


777 


52 


9 


072 


098 


.0368 


764 


51 


10 


.44098 


.49134 


2.0353 


.89752 


50 


11 


124 


170 


.0338 


739 


49 


12 


151 


206 


.0323 


726 


48 


13 


177 


242 


.0308 


713 


47 


14 


203 


278 


.0293 


700 


46 


15 


.44229 


.49315 


2.0278 


.89687 


45 


16 


255 


351 


.0263 


674 


44 


17 


281 


387 


.0248 


662 


43 


18 


307 


423 


.0233 


649 


42 


19 


333 


459 


.0219 


636 


41 


20 


.44359 


.49495 


2.0204 


.89623 


40 


21 


385 


532 


.0189 


610 


39 


22 


411 


568 


.0174 


597 


38 


23 


437 


604 


.0160 


584 


37 


24 


464 


640 


.0145 


571 


36 


25 


.44490 


.49677 


2.0130 


.89558 


35 


26 


516 


713 


.0115 


545 


34 


27 


542 


749 


.0101 


532 


33 


28 


568 


786 


.0086 


519 


32 


29 


594 


822 


.0072 


506 


31 


30 


.44620 


.49858 


2.0057 


.89493 


30 


31 


646 


894 


.0042 


480 


29 


32 


672 


931 


.0028 


467 


28 


33 


698 


.49967 


2.0013 


454 


27 


34 


724 


.50004 


1.9999 


441 


26 


35 


.44750 


.50040 


1.9984 


.89428 


25 


36 


776 


076 


.9970 


415 


24 


37 


802 


113 


.9955 


402 


23 


38 


828 


149 


.9941 


389 


22 


39 


854 


185 


.9926 


376 


21 


40 


.44880 


.50222 


1.9912 


.89363 


20 


41 


906 


258 


.9897 


350 


19 


42 


932 


295 


.9883 


337 


18 


43 


958 


331 


.9868 


324 


17 


44 


.44984 


368 


.9854 


311 


16 


45 


.45010 


.50404 


1.9840 


.89298 


15 


46 


036 


441 


.9825 


285 


14 


47 


062 


477 


.9811 


272 


13 


48 


088 


514 


.9797 


259 


12 


49 


114 


550 


.9782 


245 


11 


50 


.45140 


.50587 


1.9768 


.89232 


10 


51 


166 


623 


.9754 


219 


9 


52 


192 


660 


.9740 


206 


8 


53 


218 


696 


.9725 


193 


7 


54 


243 


733 


.9711 


180 


6 


55 


.45269 


.50769 


1.9697 


.89167 


5 


56 


295 


806 


.9683 


153 


4 


57 


321 


843 


.9669 


140 


3 


58 


347 


879 


.9654 


127 


2 


59 


373 


916 


.9640 


114 


1 


60 


.45399 


.50953 


1.9626 


.89101 







Cos 


Ctn 


Tan 


Sin 


/ 



rr 


Sin 


Tan 


Ctn 


Cos 







.45399 


.50953 


1.9626 


.89101 


60 


i 


425 


.50989 


.9612 


087 


59 


2 


451 


.51026 


.9598 


074 


58 


3 


477 


063 


.9584 


061 


57 


4 


503 


099 


.9570 


048 


56 


5 


.45529 


.51136 


1.9556 


.89035 


55 


6 


554 


173 


.9542 


021 


54 


7 


580 


209 


.9528 


.89008 


53 


8 


606 


246 


.9514 


.88995 


52 


9 


632 


283 


.9500 


981 


51 


10 


.45658 


.51319 


1.9486 


.88968 


50 


11 


684 


356 


.9472 


955 


49 


12 


710 


393 


.9458 


942 


48 


13 


736 


430 


.9444 


928 


47 


14 


762 


467 


.9430 


915 


46 


15 


.45787 


.51503 


1.9416 


.88902 


45 


16 


813 


540 


.9402 


888 


44 


17 


839 


577 


.9388 


875 


43 


18 


865 


614 


.9375 


862 


42 


19 


891 


651 


.9361 


848 


41 


20 


.45917 


.51688 


1.9347 


.88835 


40 


21 


942 


724 


.9333 


822 


39 


22 


968 


761 


.9319 


808 


38 


23 


.45994 


798 


.9306 


795 


37 


24 


.46020 


835 


.9292 


782 


36 


25 


.46046 


.51872 


1.9278 


.88768 


35 


26 


072 


909 


.9265 


755 


34 


27 


097 


946 


.9251 


741 


33 


28 


123 


.51983 


.9237 


728 


32 


29 


149 


.52020 


.9223 


715 


31 


30 


.46175 


.52057 


1.9210 


.88701 


30 


31 


201 


094 


.9196 


688 


29 


32 


226 


131 


.9183 


674 


28 


33 


252 


168 


.9169 


661 


27 


34 


278 


205 


.9155 


647 


26 


35 


.46304 


.52242 


1.9142 


.88634 


25 


36 


330 


279 


.9128 


620 


24 


37 


355 


316 


.9115 


607 


23 


38 


381 


353 


.9101 


593 


22 


39 


407 


390 


.9088 


580 


21 


40 


.46433 


.52427 


1.9074 


.88566 


20 


41 


458 


464 


.9061 


553 


19 


42 


484 


501 


.9047 


539 


18 


43 


510 


538 


.9034 


526 


17 


44 


536 


575 


.9020 


512 


16 


45 


.46561 


.52613 


1.9007 


.88499 


15 


46 


587 


650 


.8993 


. 485 


14 


47 


613 


687 


.8980 


472 


13 


48 


639 


724 


.8967 


458 


12 


49 


664 


761 


.8953 


445 


11 


50 


.46690 


.52798 


1.8940 


.88431 


10 


51 


716 


836 


.8927 


417 


9 


52 


742 


873 


.8913 


404 


8 


53 


767 


910 


.8900 


390 


7 


54 


793 


947 


.8887 


377 


6 


55 


.46819 


.52985 


1.8873 


.88363 


5 


56 


844 


.53022 


.8860 


349 


4 


57 


870 


059 


.8847 


336 


3 


58 


896 


096 


.8834 


322 


2 


59 


921 


134 


.8820 


308 


1 


60 


.46947 


.53171 


1.8807 


.88295 







Cos 


Ctn 


Tan 


Sin 


/ 



63' 



62° 



36 



28° — Values of Trigonometric Functions — 29' 



PI 



/ 


Sin 


Tan 


Ctn 


Cos 







.46947 


.53171 


1.8807 


.88295 


60 


1 


973 


208 


.8794 


281 


59 


2 


.46999 


246 


.8781 


267 


58 


3 


.47024 


283 


.8768 


254 


57 


4 


050 


320 


.8755 


240 


56 


5 


.47076 


.53358 


1.8741 


.88226 


55 


6 


101 


395 


.8728 


213 


54 


7 


127 


432 


.8715 


199 


53 


8 


153 


470 


.8702 


185 


52 


9 


178 


507 


.8689 


172 


51 


10 


.47204 


.53545 


1.8676 


.88158 


50 


11 


229 


582 


.8663 


144 


49 


12 


255 


620 


.8650 


130 


48 


13 


281 


657 


.8637 


117 


47 


14 


306 


694 


.8624 


103 


46 


15 


.47332 


.53732 


1.8611 


.88089 


45 


16 


358 


769 


.8598 


075 


44 


17 


383 


807 


.8585 


062 


43 


18 


409 


844 


.8572 


048 


42 


19 


434 


882 


.8559 


034 


41 


20 


.47460 


.53920 


1.8546 


.88020 


40 


21 


486 


957 


.8533 


.88006 


39 


22 


511 


.53995 


.8520 


.87993 


38 


23 


537 


.54032 


.8507 


979 


37 


24 


562 


070 


.8495 


965 


36 


25 


.47588 


.54107 


1.8482 


.87951 


35 


26 


614 


145 


.8469 


937 


34 


27 


639 


183 


.8456 


923 


33 


28 


665 


220 


.8443 


909 


32 


29 


690 


258 


.8430 


896 


31 


30 


.47716 


.54296 


1.8418 


.87882 


30 


31 


741 


333 


.8405 


868 


29 


32 


767 


371 


.8392 


854 


28 


33 


793 


409 


.8379 


840 


27 


34 


818 


446 


.8367 


826 


26 


35 


.47844 


.54484 


1.8354 


.87812 


25 


36 


869 


522 


.8341 


798 


24 


37 


895 


560 


.8329 


784 


23 


38 


920 


597 


.8316 


770 


22 


39 


946 


635 


.8303 


756 


21 


40 


.47971 


.54673 


1.8291 


.87743 


20 


41 


.47997 


711 


.8278 


729 


19 


42 


.48022 


748 


.8265 


715 


18 


43 


048 


786 


.8253 


701 


17 


44 


073 


824 


.8240 


687 


16 


45 


.48099 


.54862 


1.8228 


.87673 


15 


46 


124 


900 


.8215 


659 


14 


47 


150 


938 


.8202 


645 


13 


48 


175 


.54975 


.8190 


631 


12 


49 


201 


.55013 


.8177 


617 


11 


50 


.48226 


.55051 


1.8165 


.87603 


10 


51 


252 


089 


.8152 


589 


9 


52 


277 


127 


.8140 


575 


8 


53 


303 


165 


.8127 


561 


7 


54 


328 


203 


.8115 


546 


6 


55 


.48354 


.55241 


1.8103 


.87532 


5 


56 


379 


279 


.8090 


518 


4 


57 


405 


317 


.8078 


504 


3 


58 


430 


355 


.8065 


490 


2 


59 


456 


393 


.8053 


476 


1 


60 


.48481 


.55431 


1.8040 


.87462 







Cos 


Ctn 


Tan 


Sin 


t 



i 


Sin 


Tan 


Ctn 


Cos 







.48481 


.55431 


1.8040 


.87462 


60 


1 


506 


469 


.8028 


448 


59 


2 


532 


507 


.8016 


434 


58 


3 


557 


545 


.8003 


420 


57 


4 


583 


583 


.7991 


406 


56 


5 


.48608 


.55621 


1.7979 


.87391 


55 


6 


634 


659 


.7966 


377 


54 


7 


659 


697 


.7954 


363 


53 


8 


684 


736 


.7942 


349 


52 


9 


710 


774 


.7930 


335 


51 


10 


.48735 


.55812 


1.7917 


.87321 


50 


11 


761 


850 


.7905 


306 


49 


12 


786 


888 


.7893 


292 


48 


13 


811 


926 


.7881 


278 


47 


14 


837 


.55964 


.7868 


264 


46 


15 


.48862 


.56003 


1.7856 


.87250 


45 


16 


888 


041 


.7844 


235 


44 


17 


913 


079 


.7832 


221 


43 


18 


938 


11.7 


.7820 


207 


42 


19 


964 


156 


.7808 


193 


41 


20 


.48989 


.56194 


1.7796 


.87178 


40 


21 


.49014 


232 


.7783 


164 


39 


22 


040 


270 


.7771 


150 


38 


23 


065 


309 


.7759 


136 


37 


24 


090 


347 


.7747 


121 


36 


25 


.49116 


.56385 


1.7735 


.87107 


35 


26 


141 


424 


.7723 


093 


34 


27 


166 


462 


.7711 


079 


33 


28 


192 


501 


.7699 


064 


32 


29 


217 


539 


.7687 


050 


31 


30 


.49242 


.56577 


1.7675 


.87036 


30 


31 


268 


616 


.7663 


021 


29 


32 


293 


654 


.7651 


.87007 


28 


33 


318 


693 


.7639 


.86993 


27 


34 


344 


731 


.7627 


978 


26 


35 


.49369 


.56769 


1.7615 


.86964 


25 


36 


394 


808 


.7603 


949 


24 


37 


419 


846 


.7591 


935 


23 


38 


445 


885 


.7579 


921 


22 


39 


470 


923 


.7567 


906 


21 


40 


.49495 


.56962 


1.7556 


.86892 


20 


41 


521 


.57000 


.7544 


878 


19 


42 


546 


039 


.7532 


863 


18 


43 


571 


078 


.7520 


849 


17 


44 


596 


116 


.7508 


834 


16 


45 


.49622 


.57155 


1.7496 


.86820 


15 


46 


647 


193 


.7485 


805 


14 


47 


672 


232 


.7473 


791 


13 


48 


697 


271 


.7461 


777 


12 


49 


723 


309 


.7449 


762 


11 


50 


.49748 


.57348 


1.7437 


.86748 


10 


51 


773 


386 


.7426 


733 


9 


52 


798 


425 


.7414 


719 


8 


53 


824 


464 


.7402 


704 


7 


54 


849 


503 


.7391 


690 


6 


55 


.49874 


.57541 


1.7379 


.86675 


5 


56 


899 


580 


.7367 


661 


4 


57 


924 


619 


.7355 


646 


3 


58 


950 


657 


.7344 


632 


2 


59 


.49975 


696 


.7332 


617 


1 


60 


.50000 


.57735 


1.7321 


.86603 







Cos 


Ctn 


Tan 


Sin 


/ 



.61° 



60° 



II] 30° — Values of Trigonometric Functions — 31' 



37 



/ 


Sin 


Tan 


Ctn 


Cos 







.50000 


.57735 


1.7321 


.86603 


60 


1 


025 


774 


.7309 


588 


59 


2 


050 


813 


.7297 


573 


58 


3 


076 


851 


.7286 


559 


57 


4 


101 


890 


.7274 


544 


56 


5 


.50126 


.57929 


1.7262 


.86530 


55 


6 


151 


.57968 


.7251 


515 


54 


7 


176 


.58007 


.7239 


501 


53 


8 


201 


046 


.7228 


486 


52 


9 


227 


085 


.7216 


471 


51 


10 


.50252 


.58124 


1.7205 


.86457 


50 


11 


277 


162 


.7193 


442 


49 


12 


302 


201 


.7182 


427 


48 


13 


327 


240 


.7170 


413 


47 


14 


352 


279 


.7159 


398 


46 


15 


.50377 


.58318 


1.7147 


.86384 


45 


16 


403 


357 


.7136 


369 


44 


17 


428 


396 


.7124 


354 


43 


18 


453 


435 


.7113 


340 


42 


19 


478 


474 


.7102 


325 


41 


20 


.50503 


.58513 


1.7090 


.86310 


40 


21 


528 


552 


.7079 


295 


39 


22 


553 


591 


.7067 


281 


38 


23 


578 


631 


.7056 


266 


37 


24 


603 


670 


.7045 


251 


36 


25 


.50628 


.58709 


1.7033 


.86237 


35 


26 


654 


748 


.7022 


222 


34 


27 


679 


787 


.7011 


207 


33 


28 


704 


826 


.6999 


192 


32 


29 


729 


865 


.6988 


178 


31 


30 


.50754 


.58905 


1.6977 


.86163 


30 


31 


779 


944 


.6965 


148 


29 


32 


804 


.58983 


.6954 


133 


28 


33 


829 


.59022 


.6943 


119 


27 


34 


854 


061 


.6932 


104 


26 


35 


.50879 


.59101 


1.6920 


.86089 


25 


36 


904 


140 


.6909 


074 


24 


37 


929 


179 


.6898 


059 


23 


38 


954 


218 


.6887 


045 


22 


39 


.50979 


258 


.6875 


030 


21 


40 


.51004 


.59297 


1.6864 


.86015 


20 


41 


029 


336 


.6853 


.86000 


19 


42 


054 


376 


.6842 


.85985 


18 


43 


079 


415 


.6831 


970 


17 


44 


104 


454 


.6820 


956 


16 


45 


.51129 


.59494 


1.6808 


.85941 


15 


46 


154 


533 


.6797 


926 


14 


47 


179 


573 


.6786 


911 


13 


48 


204 


612 


.6775 


896 


12 


49 


229 


651 


.6764 


881 


11 


50 


.51254 


.59691 


1.6753 


.85866 


10 


51 


279 


730 


.6742 


851 


9 


52 


304 


770 


.6731 


836 


8 


53 


329 


809 


.6720 


821 


7 


54 


354 


849 


.6709 


806 


6 


55 


.51379 


.59888 


1.6698 


.85792 


5 


56 


404 


928 


.6687 


777 


4 


57 


429 


.59967 


.6676 


762 


3 


58 


454 


.60007 


.6665 


747 


2 


59 


479 


046 


.6654 


732 


1 


60 


.51504 


.60086 


1.6643 


.85717 





Cos 


Ctn 


Tan 


Sin 


t 



/ 


Sin 


Tan 


Ctn 


Cos 







.51504 


.60086 


1.6643 


.85717 


60 


1 


529 


126 


.6632 


702 


59 


2 


554 


165 


.6621 


687 


58 


3 


579 


205 


.6610 


672 


57 


4 


604 


245 


.6599 


657 


56 


5 


.51628 


.60284 


1.6588 


.85642 


55 


6 


653 


324 


.6577 


627 


54 


7 


678 


364 


.6566 


612 


53 


8 


703 


403 


.6555 


597 


52 


9 


728 


443 


.6545 


582 


51 


10 


.51753 


.60483 


1.6534 


.85567 


50 


11 


778 


522 


.6523 


551 


49 


12 


803 


562 


.6512 


536 


48 


13 


828 


602 


.6501 


521 


47 


14 


852 


642 


.6490 


506 


46 


15 


.51877 


.60681 


1.6479 


.85491 


45 


16 


902 


721 


.6469 


476 


44 


17 


927 


761 


.6458 


461 


43 


18 


952 


801 


.6447 


446 


42 


19 


.51977 


841 


.6436 


431 


41 


20 


.52002 


.60881 


1.6426 


.85416 


40 


21 


026 


921 


.6415 


401 


39 


22 


051 


.60960 


.6404 


385 


38 


23 


076 


.61000 


.6393 


370 


37 


24 


101 


040 


.6383 


355 


36 


25 


.52126 


.61080 


1.6372 


.85340 


35 


26 


151 


120 


.6361 


325 


34 


27 


175 


160 


.6351 


310 


33 


28 


200 


200 


.6340 


294 


32 


29 


225 


240 


.6329 


279 


31 


30 


.52250 


.61280 


1.6319 


.85264 


30 


31 


275 


320 


.6308 


249 


29 


32 


299 


360 


.6297 


234 


28 


33 


324 


400 


.6287 


218 


27 


34 


349 


440 


.6276 


203 


26 


35 


.52374 


.61480 


1.6265 


.85188 


25 


36 


399 


520 


.6255 


173 


24 


37 


423 


561 


.6244 


157 


23 


38 


448 


601 


.6234 


142 


22 


39 


473 


641 


.6223 


127 


21 


40 


.52498 


.61681 


1.6212 


.85112 


20 


41 


522 


721 


.6202 


096 


19 


42 


547 


761 


.6191 


081 


18 


43 


572 


801 


.6181 


066 


17 


44 


597 


842 


.6170 


051 


16 


45 


.52621 


.61882 


1.6160 


.85035 


15 


46 


b46 


922 


.6149 


020 


14 


47 


671 


.61962 


.6139 


.85005 


13 


48 


696 


.62003 


.6128 


.84989 


12 


49 


720 


043 


.6118 


974 


11 


50 


.52745 


.62083 


1.6107 


.84959 


10 


51 


770 


124 


.6097 


943 


9 


52 


794 


164 


.6087 


928 


8 


53 


819 


204 


.6076 


913 


7 


54 


844 


245 


.6066 


897 


6 


55 


.52869 


.62285 


1.6055 


.84882 


5 


56 


893 


325 


.6045 


866 


4 


57 


918 


366 


.6034 


851 


3 


58 


943 


406 


.6024 


836 


2 


59 


967 


446 


.6014 


820 


1 


60 


.52992 


.62487 


1.6003 


.84805 







Cos 


Ctn 


Tan 


Sin 


/ 



59' 



58" 



38 



32° — Values of Trigonometric Functions — 33 ( 



[H 



10 

ii 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



Sin Tan Ctn Cos 



.52992 

.53017 

041 

066 

091 

.53115 
140 
164 
189 
214 

.53238 
263 
288 
312 
337 

.53361 
386 
411 
435 
460 

.53484 
509 
534 

558 
583 

.53607 
632 
656 
681 
705 

.53730 

754 
779 
804 

828 

.53853 

877 
902 
926 
951 

.53975 

.54000 

024 

049 

073 

.54097 
122 
146 
171 
195 

.54220 
244 
269 
293 
317 

.54342 
366 
391 
415 
440 

.54464 



.62487 
527 
568 
608 
649 

.62689 
730 
770 
811 
852 

.62892 

933 

.62973 

.63014 

055 

.63095 
136 
177 
217 

258 

.63299 
340 
380 
421 
462 

.63503 
544 

584 
625 
666 

.63707 

748 
789 
830 

871 

.63912 

953 

.63994 

.64035 

076 

.64117 
158 

199 
240 
281 

.64322 
363 
404 
446 

487 

.64528 
569 
610 
652 
693 

.64734 
775 
817 
858 
899 

.64941 



1.6003 
.5993 
.5983 
.5972 
.5962 

1.5952 
.5941 
.5931 
.5921 
.5911 

1.5900 
.5890 
.5880 
.5869 
.5859 

1.5849 
.5839 
.5829 

.5818 
.5808 

1.5798 

.5788 
.5778 
.5768 
.5757 

1.5747 
.5737 
.5727 
.5717 
.5707 

1.5697 
.5687 
.5677 
.5667 
.5657 

1.5647 

.5637 
.5627 
.5617 
.5607 

1.5597 

.5587 
.5577 
.5567 
.5557 

1.5547 
.5537 
.5527 
.5517 
.5507 

1.5497 
.5487 
.5477 
.5468 
.5458 

1.5448 
.5438 
.5428 
.5418 
.5408 

1.5399 



Cos Ctn Tan 

g 7 o 



.84805 
789 
774 
759 
743 

.84728 
712 
697 
681 
666 

.84650 
635 
619 
604 

588 

.84573 
557 
542 
526 
511 

.84495 
480 
464 
448 
433 

.84417 
402 
386 
370 
355 

.84339 
324 
308 
292 

277 

.84261 
245 
230 
214 
198 

.84182 
167 
151 
135 
120 

.84104 
088 
072 
057 
041 

.84025 

.84009 

.83994 

978 

962 

.83946 
930 
915 
899 

883 
.83867 



Sin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 

7 
6 

5 

4 
3 
2 
1 





/ 


Sin 


Tan 


Ctn 


Cos 







.54464 


.64941 


1.5399 


.83867 


60 


1 


488 


.64982 


.5389 


851 


59 


2 


513 


.65024 


.5379 


835 


58 


3 


537 


065 


.5369 


819 


57 


4 


561 


106 


.5359 


804 


56 


5 


.54586 


.65148 


1.5350 


.83788 


55 


6 


610 


189 


.5340 


772 


54 


7 


635 


231 


.5330 


756 


53 


8 


659 


272 


.5320 


740 


52 


9 


683 


314 


.5311 


724 


51 


10 


.54708 


.65355 


1.5301 


.83708 


50 


11 


732 


397 


.5291 


692 


49 


12 


756 


438 


.5282 


676 


48 


13 


781 


480 


.5272 


660 


47 


14 


805 


521 


.5262 


645 


46 


15 


.54829 


.65563 


1.5253 


.83629 


45 


16 


854 


604 


.5243 


613 


44 


17 


878 


646 


.5233 


597 


43 


18 


902 


688 


.5224 


581 


42 


19 


927 


729 


.5214 


565 


41 


20 


.54951 


.65771 


1.5204 


.83549 


40 


21 


975 


813 


.5195 


533 


39 


22 


.54999 


854 


.5185 


517 


38 


23 


.55024 


896 


.5175 


501 


37 


24 


048 


938 


.5166 


485 


36 


25 


.55072 


.65980 


1.5156 


.83469 


35 


26 


097 


.66021 


.5147 


453 


34 


27 


121 


063 


.5137 


437 


33 


28 


145 


105 


.5127 


421 


32 


29 


169 


147 


.5118 


405 


31 


30 


.55194 


.66189 


1.5108 


.83389 


30 


31 


218 


230 


.5099 


373 


29 


32 


242 


272 


.5089 


356 


28 


33 


266 


314 


.5080 


340 


27 


34 


291 


356 


.5070 


324 


26 


35 


.55315 


.66398 


1.5061 


.83308 


25 


36 


339 


440 


.5051 


292 


24 


37 


363 


482 


.5042 


276 


23 


38 


388 


524 


.5032 


260 


22 


39 


412 


566 


.5023 


244 


21 


40 


.55436 


.66608 


1.5013 


.83228 


20 


41 


460 


650 


.5004 


212 


19 


42 


484 


692 


.4994 


195 


18 


43 


509 


734 


.4985 


179 


17 


44 


533 


776 


.4975 


163 


16 


45 


.55557 


.66818 


1.4966 


.83147 


15 


46 


581 


860 


.4957 


131 


14 


47 


605 


902 


.4947 


115 


13 


48 


630 


944 


.4938 


098 


12 


49 


654 


.66986 


.4928 


082 


11 


50 


.55678 


.67028 


1.4919 


.83066 


10 


51 


702 


071 


.4910 


050 


9 


52 


726 


113 


.4900 


034 


8 


53 


750 


155 


.4891 


017 


7 


54 


775 


197 


.4882 


.83001 


6 


55 


.55799 


.67239 


1.4872 


.82985 


5 


56 


823 


282 


.4863 


969 


4 


57 


847 


324 


.4854 


953 


3 


58 


871 


366 


.4844 


936 


2 


59 


895 


409 


.4835 


920 


1 


60 


.55919 


.67451 


1.4826 


.82904 







Cos 


Ctn 


Tan 


Sin 


/ 



56< 



II] 34° — Values of Trigonometric Functions — 35 ( 



3<J 



o 

1 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 



46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



Sin 



.55919 

943 

968 

.55992 

.56016 

.56040 
064 
088 
112 
136 

.56160 
184 
208 
232 
256 

.56280 
305 
329 
353 
377 

.56401 
425 
449 
473 
497 

.56521 
545 
569 
593 
617 

.56641 
665 
689 
713 
736 

.56760 
784 
808 
832 
856 

.56880 
904 
928 
952 

.56976 



45 .57000 



024 
047 
071 
095 

.57119 
143 
167 
191 
215 

.57238 
262 
286 
310 
334 

.57358 



Tan Ctn Cos 



.67451 
493 
536 

578 
620 

.67663 

705 
748 
790 
832 

.67875 

917 

.67960 

.68002 

045 

.68088 
130 
173 
215 
258 

.68301 
343 
386 
429 
471 

.68514 
557 
600 
642 
685 

.68728 
771 
814 

857 
900 

.68942 

.68985 

.69028 

071 

114 

.69157 
200 
243 
286 
329 

.69372 
416 
459 
502 
545 

.69588 
631 
675 
718 
761 

.69804 
847 
891 
934 

.69977 

.70021 



1.4826 
.4816 
.4807 
.4798 

.4788 

1.4779 
.4770 
.4761 
.4751 
.4742 

1.4733 
.4724 
.4715 
.4705 
.4696 

1.4687 
.4678 
.4669 
.4659 
.4650 

1.4641 
.4632 
.4623 
.4614 
.4605 

1.4596 
.4586 
.4577 
.4568 
.4559 

1.4550 
.4541 
.4532 
.4523 
.4514 

1.4505 
.4496 
.4487 

.4478 
.4469 

1.4460 
.4451 
.4442 
.4433 
.4424 

1.4415 
.4406 
.4397 

.4388 
.4379 

1.4370 
.4361 
.4352 
.4344 
.4335 

1.4326 
.4317 
.4308 
.4299 
.4290 

1.4281 



.82904 
887 
871 
855 
839 

.82822 
806 
790 
773 
757 

.82741 
724 
708 
692 
675 

.82659 
643 
626 
610 
593 

.82577 
561 
544 
528 
511 

.82495 
478 
462 
446 
429 

.82413 
396 
380 
363 
347 

.82330 
314 
297 
281 
264 

.82248 
231 
214 
198 
181 

.82165 
148 
132 
115 
098 

.82082 
065 
048 
032 

.82015 

.81999 
982 
965 
949 
932 

.81915 



Cos Ctn Tan Sin 
55° 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 

2 
1 





/ 




Sin 


Tan 


Ctn 


Cos 




.57358 


.70021 


1.4281 


.81915 


60 


1 


381 


064 


.4273 


899 


59 


2 


405 


107 


.4264 


882 


58 


3 


429 


151 


.4255 


865 


57 


4 


453 


194 


.4246 


848 


56 


5 


.57477 


.70238 


1.4237 


.81832 


55 


6 


501 


281 


.4229 


815 


54 


7 


524 


325 


.4220 


798 


53 


8 


548 


368 


.4211 


782 


52 


9 


572 


412 


.4202 


765 


51 


10 


.57596 


.70455 


1.4193 


.81748 


50 


11 


619 


499 


.4185 


731 


49 


12 


643 


542 


.4176 


714 


48 


13 


667 


586 


.4167 


698 


47 


14 


691 


629 


.4158 


681 


46 


15 


.57715 


.70673 


1.4150 


.81664 


45 


16 


738 


717 


.4141 


647 


44 


17 


762 


760 


.4132 


631 


43 


18 


786 


804 


.4124 


614 


42 


19 


810 


848 


.4115 


597 


41 


20 


.57833 


.70891 


1.4106 


.81580 


40 


21 


857 


935 


.4097 


563 


39 


22 


881 


.70979 


.4089 


546 


38 


23 


904 


.71023 


.4080 


530 


37 


24 


928 


066 


.4071 


513 


36 


25 


.57952 


.71110 


1.4063 


.81496 


35 


26 


976 


154 


.4054 


479 


34 


27 


.57999 


198 


.4045 


462 


33 


28 


.58023 


242 


.4037 


445 


32 


29 


047 


285 


.4028 


428 


31 


30 


.58070 


.71329 


1.4019 


.81412 


30 


31 


094 


373 


.4011 


395 


29 


32 


118 


417 


.4002 


378 


28 


33 


141 


461 


.3994 


361 


27 


34 


165 


505 


.3985 


344 


26 


35 


.58189 


.71549 


1.3976 


.81327 


25 


36 


212 


593 


.3968 


310 


24 


37 


236 


637 


.3959 


293 


23 


38 


260 


681 


.3951 


276 


22 


39 


283 


725 


.3942 


259 


21 


40 


.58307 


.71769 


1.3934 


.81242 


20 


41 


330 


813 


.3925 


225 


19 


42 


354 


857 


.3916 


208 


18 


43 


378 


901 


.3908 


191 


17 


44 


401 


946 


.3899 


174 


16 


45 


.58425 


.71990 


1.3891 


.81157 


15 


46 


449 


.72034 


.3882 


140 


14 


47 


472 


078 


.3874 


123 


13 


48 


496 


122 


.3865 


106 


12 


49 


519 


167 


.3857 


089 


11 


50 


.58543 


.72211 


1.3848 


.81072 


10 


51 


567 


255 


.3840 


055 


9 


52 


590 


299 


.3831 


038 


8 


53 


614 


344 


.3823 


021 


7 


54 


637 


388 


.3814 


.81004 


6 


55 


.58661 


.72432 


1.3806 


.80987 


5 


56 


684 


477 


.3798 


970 


4 


57 


708 


521 


.3789 


953 


3 


58 


731 


565 


.3781 


936 


2 


59 


755 


610 


.3772 


919 


1 


60 


.58779 


.72654 


1.3764 


.80902 




1 




Cos 


Ctn 


Tan 


Sin 



54° 



40 



36° — Values of Trigonometric Functions — 37° 



[II 



/ 


Sin 


Tan 


Ctn 


Cos 







.58779 


.72654 


1.3764 


.80902 


60 


1 


802 


699 


.3755 


885 


59 


2 


826 


743 


.3747 


867 


58 


3 


849 


788 


.3739 


850 


57 


4 


873 


832 


.3730 


833 


56 


5 


.58896 


.72877 


1.3722 


.80816 


55 


6 


920 


921 


.3713 


799 


54 


7 


943 


.72966 


.3705 


782 


53 


8 


967 


.73010 


.3697 


765 


52 


9 


.58990 


055 


.3688 


748 


51 


10 


.59014 


.73100 


1.3680 


.80730 


50 


11 


037 


144 


.3672 


713 


49 


12 


061 


189 


.3663 


696 


48 


13 


084 


234 


.3655 


679 


47 


14 


108 


278 


.3647 


662 


46 


15 


.59131 


.73323 


1.3638 


.80644 


45 


16 


154 


368 


.3630 


627 


44 


17 


178 


413 


.3622 


610 


43 


18 


201 


457 


.3613 


593 


42 


19 


225 


502 


.3605 


576 


41 


20 


.59248 


.73547 


1.3597 


.80558 


40 


21 


272 


592 


.3588 


541 


39 


22 


295 


637 


.3580 


524 


38 


23 


318 


681 


.3572 


507 


37 


24 


342 


726 


.3564 


489 


36 


25 


.59365 


.73771 


1.3555 


.80472 


35 


26 


389 


816 


.3547 


455 


34 


27 


412 


861 


.3539 


438 


33 


28 


436 


906 


.3531 


420 


32 


29 


459 


951 


.3522 


403 


31 


30 


.59482 


.73996 


1.3514 


.80386 


30 


31 


506 


.74041 


.3506 


368 


29 


32 


529 


086 


.3498 


351 


28 


33 


552 


131 


.3490 


334 


27 


34 


576 


176 


.3481 


316 


26 


35 


.59599 


.74221 


1.3473 


.80299 


25 


36 


622 


267 


.3465 


282 


24 


37 


646 


312 


.3457 


264 


23 


38 


669 


357 


.3449 


247 


22 


39 


693 


402 


.3440 


230 


21 


40 


.59716 


.74447 


1.3432 


.80212 


20 


41 


739 


492 


.3424 


195 


19 


42 


763 


538 


.3416 


178 


18 


43 


786 


583 


.3408 


160 


17 


44 


809 


628 


.3400 


143 


16 


45 


.59832 


.74674 


1.3392 


.80125 


15 


46 


856 


719 


.3384 


108 


14 


47 


879 


764 


.3375 


091 


13 


48 


902 


810 


.3367 


073 


12 


49 


926 


855 


.3359 


056 


11 


50 


.59949 


.74900 


1.3351 


.80038 


10 


51 


972 


946 


.3343 


021 


9 


52 


.59995 


.74991 


.3335 


.80003 


8 


53 


.60019 


.75037 


.3327 


.79986 


7 


54 


042 


082 


.3319 


968 


6 


55 


.60065 


.75128 


1.3311 


.79951 


5 


56 


089 


173 


.3303 


934 


4 


57 


112 


219 


.3295 


916 


3 


58 


135 


264 


.3287 


899 


2 


59 


158 


310 


.3278 


881 


1 


60 


.60182 


.75355 


1.3270 


.79864 





Cos 


Ctn 


Tan 


Sin 



/ 



Sin 


Tan 


Ctn 


Cos 




.60182 


.75355 


1.3270 


.79864 


60 


1 


205 


401 


.3262 


846 


59 


2 


228 


447 


.3254 


829 


58 


3 


251 


492 


.3246 


811 


57 


4 


274 


538 


.3238 


793 


56 


5 


.60298 


.75584 


1.3230 


.79776 


55 


6 


321 


629 


.3222 


758 


54 


7 


344 


675 


.3214 


741 


53 


8 


367 


721 


.3206 


723 


52 


9 


390 


767 


.3198 


706 


51 


10 


.60414 


.75812 


1.3190 


.79688 


50 


11 


437 


858 


.3182 


671 


49 


12 


460 


904 


.3175 


653 


48 


13 


483 


950 


.3167 


635 


47 


14 


506 


.75996 


.3159 


618 


46 


15 


.60529 


.76042 


1.3151 


.79600 


45 


16 


553 


088 


.3143 


583 


44 


17 


576 


134 


.3135 


565 


43 


18 


599 


180 


.3127 


547 


42 


19 


622 


226 


.3119 


530 


41 


20 


.60645 


.76272 


1.3111 


.79512 


40 


21 


668 


318 


.3103 


494 


39 


22 


691 


364 


.3095 


477 


38 


23 


714 


410 


.3087 


459 


37 


24 


738 


456 


.3079 


441 


36 


25 


.60761 


.76502 


1.3072 


.79424 


35 


26 


784 


548 


.3064 


406 


34 


27 


807 


594 


.3056 


388 


33 


28 


830 


640 


.3048 


371 


32 


29 


853 


686 


.3040 


353 


31 


30 


.60876 


.76733 


1.3032 


.79335 


30 


31 


899 


779 


.3024 


318 


29 


32 


922 


825 


.3017 


300 


28 


33 


945 


871 


.3009 


282 


27 


34 


968 


918 


.3001 


264 


26 


35 


.60991 


.76964 


1.2993 


.79247 


25 


36 


.61015 


.77010 


.2985 


229 


24 


37 


038 


057 


.2977 


211 


23 


38 


061 


103 


.2970 


193 


22 


39 


084 


149 


.2962 


176 


21 


40 


.61107 


.77196 


1.2954 


.79158 


20 


41 


130 


242 


.2946 


140 


19 


42 


153 


289 


.2938 


122 


18 


43 


176 


335 


.2931 


105 


17 


44 


199 


382 


.2923 


087 


16 


45 


.61222 


.77428 


1.2915 


.79069 


15 


46 


245 


475 


.2907 


051 


14 


47 


268 


521 


.2900 


033 


13 


48 


291 


568 


.2892 


.79016 


12 


49 


314 


615 


.2884 


.78998 


11 


50 


.61337 


.77661 


1.2876 


.78980 


10 


51 


360 


708 


.2869 


962 


9 


52 


383 


754 


.2861 


944 


8 


53 


406 


801 


.2853 


926 


7 


54 


429 


. 848 


.2846 


908 


6 


55 


.61451 


.77895 


1.2838 


.78891 


5 


56 


474 


941 


.2830 


873 


4 


57 


497 


.77988 


.2822 


855 


3 


58 


520 


.78035 


.2815 


837 


2 


59 


543 


082 


.2807 


819 


1 


60 


.61566 


.78129 


1.2799 


.78801 







Cos 


Ctn 


Tan 


Sin 


/ 



53< 



52° 



II] 38° — Values of Trigonometric Functions — 39' 



41 



/ 


Sin 


Tan 


Ctn 


Cos 


60 





.61566 


.78129 


1.2799 


.78801 


1 


589 


175 


.2792 


783 


59 


2 


612 


222 


'.2784 


765 


58 


3 


635 


269 


.2776 


747 


57 


4 


658 


316 


.2769 


729 


56 


5 


.61681 


.78363 


1.2761 


.78711 


55 


6 


704 


410 


.2753 


694 


54 


7 


726 


457 


.2746 


676 


53 


8 


749 


504 


.2738 


658 


52 


9 


772 


551 


.2731 


640 


51 


10 


.61795 


.78598 


1.2723 


.78622 


50 


11 


818 


645 


.2715 


604 


49 


12 


841 


692 


.2708 


586 


48 


13 


864 


739 


.2700 


568 


47 


14 


887 


786 


.2693 


550 


46 


15 


.61909 


.78834 


1.2685 


.78532 


45 


16 


932 


881 


.2677 


514 


44 


17 


955 


928 


.2670 


496 


43 


18 


.61978 


.78975 


.2662 


478 


42 


19 


.62001 


.79022 


.2655 


460 


41 


20 


.62024 


.79070 


1.2647 


.78442 


40 


21 


046 


117 


.2640 


424 


39 


22 


069 


164 


.2632 


405 


38 


23 


092 


212 


.2624 


387 


37 


24 


115 


259 


.2617 


369 


36 


25 


.62138 


.79306 


1.2609 


.73351 


35 


26 


160 


354 


.2602 


333 


34 


27 


183 


401 


.2594 


315 


33 


28 


206 


449 


.2587 


297 


32 


29 


229 


496 


.2579 


279 


31 


30 


.62251 


.79544 


1.2572 


.78261 


30 


31 


274 


591 


.2564 


243 


29 


32 


297 


639 


.2557 


225 


28 


33 


320 


686 


.2549 


206 


27 


34 


342 


734 


.2542 


188 


26 


35 


.62365 


.79781 


1.2534 


.78170 


25 


36 


388 


829 


.2527 


152 


24 


37 


411 


877 


.2519 


134 


23 


38 


433 


924 


.2512 


116 


22 


39 


456 


.79972 


.2504 


098 


21 


40 


.62479 


.80020 


1.2497 


.78079 


20 


41 


502 


067 


.2489 


061 


19 


42 


524 


115 


.2482 


043 


18 


43 


547 


163 


.2475 


025 


17 


44 


570 


211 


.2467 


.78007 


16 


45 


.62592 


.80258 


1.2460 


.77988 


15 


46 


615 


306 


.2452 


970 


14 


47 


638 


354 


.2445 


952 


13 


48 


660 


402 


.2437 


934 


12 


49 


683 


450 


.2430 


916 


11 


50 


.62706 


,80498 


1.2423 


.77897 


10 


51 


728 


546 


.2115 


879 


9 


52 


751 


594 


.2408 


861 


8 


53 


774 


642 


.2401 


843 


7 


54 


796 


690 


.2393 


824 


6 


55 


.62819 


.80738 


1.2386 


.77806 


5 


56 


842 


786 


.2378 


788 


4 


57 


864 


834 


.2371 


769 


3 


58 


887 


882 


.2364 


751 


2 


59 


909 


930 


.2356 


733 


1 


60 


.62932 


.80978 


1.2349 


.77715 







Cos 


Ctn 


Tan 


Sin 


/ 



/ 


Sin 


Tan 


Ctn 


Cos 







.62932 


.80978 


1.2349 


.77715 


60 


1 


955 


.81027 


.2342 


696 


59 


2 


.62977 


075 


.2334 


678 


58 


3 


.63000 


123 


.2327 


660 


57 


4 


022 


171 


.2320 


641 


56 


5 


.63045 


.81220 


1.2312 


.77623 


55 


6 


068 


268 


.2305 


605 


54 


7 


090 


316 


.2298 


586 


53 


8 


113 


364 


.2290 


568 


52 


9 


135 


413 


.2283 


550 


51 


10 


.63158 


.81461 


1.2276 


.77531 


50 


11 


180 


510 


.2268 


513 


49 


12 


203 


558 


.2261 


494 


48 


13 


225 


606 


.2254 


476 


47 


14 


248 


655 


.2247 


458 


46 


15 


.63271 


.81703 


1.2239 


.77439 


45 


16 


293 


752 


.2232 


421 


44 


17 


316 


800 


.2225 


402 


43 


18 


338 


849 


.2218 


384 


42 


19 


361 


898 


.2210 


366 


41 


20 


.63383 


.81946 


1.2203 


.77347 


40 


21 


406 


.81995 


.2196 


329 


39 


22 


428 


.82044 


.2189 


310 


38 


23 


451 


092 


.2181 


292 


37 


24 


473 


141 


.2174 


273 


36 


25 


.63496 


.82190 


1.2167 


.77255 


35 


26 


518 


238 


.2160 


236 


34 


27 


540 


287 


.2153 


218 


33 


28 


563 


336 


.2145 


199 


32 


29 


585 


, 385 


.2138 


181 


31 


30 


.63608 


.82434 


1.2131 


.77162 


30 


31 


630 


483 


.2124 


144 


29 


32 


653 


531 


.2117 


125 


28 


33 


675 


580 


.2109 


107 


27 


34 


698 


629 


.2102 


088 


26 


35 


.63720 


.82678 


1.2095 


.77070 


25 


36 


742 


727 


.2088 


051 


24 


37 


765 


776 


.2081 


033 


23 


38 


787 


825 


.2074 


.77014 


22 


39 


810 


874 


.2066 


.76996 


21 


40 


.63832 


.82923 


1.2059 


.76977 


20 


41 


854 


.82972 


.2052 


959 


19 


42 


877 


.83022 


.2045 


940 


18 


43 


899 


071 


.2038 


921 


17 


44 


922 


120 


.2031 


903 


16 


45 


.63944 


.83169 


1.2024 


.76884 


15 


46 


966 


218 


.2017 


866 


14 


47 


.63989 


268 


.2009 


847 


13 


48 


.64011 


317 


.2002 


828 


12 


49 


033 


366 


.1995 


810 


11 


50 


.64056 


.83415 


1.1988 


.76791 


10 


51 


078 


465 


.1981 


772 


9 


52 


100 


514 


.1974 


754 


8 


53 


123 


564 


.1967 


735 


7 


54 


145 


613 


.1960 


717 


6 


55 


.64167 


.83662 


1.1953 


.76698 


5 


56 


190 


712 


.1946 


679 


4 


57 


212 


761 


.1939 


661 


3 


58 


234 


811 


.1932 


642 


2 


59 


256 


860 


.1925 


623 


1 


60 


.64279 


.83910 


1.1918 


.76604 







Cos 


Ctn 


Tan 


Sin 


/ 



51 



50° 



42 


40° — Values of Trigonometric Functions — 41° 


[II 


/ 


Sin 


Tan 


Ctn 


Cos 




/ 


Sin 


Tan 


Ctn 


Cos 







.64279 


.83910 


1.1918 


.76604 


60 





.65606 


.86929 


1.1504 


.75471 


60 


1 


301 


.83960 


.1910 


586 


59 


1 


628 


.86980 


.1497 


452 


59 


2 


323 


.84009 


.1903 


567 


58 


2 


650 


.87031 


.1490 


433 


58 


3 


346 


059 


.1896 


548 


57 


3 


672 


082 


.1483 


414 


57 


4 


368 


108 


.1889 


530 


56 


4 


694 


133 


.1477 


395 


56 


5 


.64390 


.84158 


1.1882 


.76511 


55 


5 


.65716 


.87184 


1.1470 


.75375 


55 


6 


412 


208 


.1875 


492 


54 


6 


738 


236 


.1463 


356 


54 


7 


435 


258 


.1868 


473 


53 


7 


759 


287 


.1456 


337 


53 


8 


457 


307 


.1861 


455 


52 


8 


781 


338 


.1450 


318 


52 


9 


479 


357 


.1854 


436 


51 


9 


803 


389 


.1443 


299 


51 


10 


.64501 


.84407 


1.1847 


.76417 


50 


10 


.65825 


.87441 


1.1436 


.75280 


50 


11 


524 


457 


.1840 


398 


49 


11 


847 


492 


.1430 


261 


49 


12 


546 


507 


.1833 


380 


48 


12 


869 


543 


.1423 


241 


48 


13 


568 


556 


.1826 


361 


47 


13 


891 


595 


.1416 


222 


47 


14 


590 


606 


.1819 


342 


46 


14 


913 


646 


.1410 


203 


46 


15 


.64612 


.84656 


1.1812 


.76323 


45 


15 


.65935 


.87698 


1.1403 


.75184 


45 


16 


635 


706 


.1806 


304 


44 


16 


956 


749 


.1396 


165 


44 


17 


657 


756 


.1799 


286 


43 


17 


.65978 


801 


.1389 


146 


43 


18 


679 


806 


.17^2 


267 


42 


18 


.66000 


852 


, .1383 


126 


42 


19 


701 


856 


.1785 


248 


41 


19 


022 


904 


.1376 


107 


41 


20 


.64723 


.84906 


1.1778 


.76229 


40 


20 


.66044 


.87955 


1.1369 


.75088 


40 


21 


746 


.84956 


.1771 


210 


39 


21 


066 


.88007 


.1363 


069 


39 


22 


768 


.85006 


.1764 


192 


38 


22 


088 


059 


.1356 


050 


38 


23 


790 


057 


.1757 


173 


37 


23 


109 


110 


.1349 


030 


37 


24 


812 


107 


.1750 


154 


36 


24 


131 


162 


.1343 


.75011 


36 


25 


.64834 


.85157 


1.1743 


.76135 


35 


25 


.66153 


.88214 


1.1336 


.74992 


35 


26 


856 


207 


.1736 


116 


34 


26 


175 


265 


.1329 


-973 


34 


27 


878 


257 


.1729 


097 


33 


27 


197 


317 


.1323 


953 


33 


28 


901 


308 


.1722 


078 


32 


28 


218 


369 


.1316 


934 


32 


29 


923 


358 


.1715 


059 


31 


29 


240 


421 


.1310 


915 


31 


30 


.64945 


.85408 


1.1708 


.76041 


30 


30 


.66262 


.88473 


1.1303 


.74896 


30 


31 


967 


458 


.1702 


022 


29 


31 


284 


524 


.1296 


876 


29 


32 


.64989 


509 


.1695 


.76003 


28 


32 


306 


576 


.1290 


857 


28 


33 


.65011 


559 


.1688 


.75984 


27 


33 


327 


628 


.1283 


838 


27 


34 


033 


609 


.1681 


965 


26 


34 


349 


680 


.1276 


818 


26 


35 


.65055 


.85660 


1.1674 


.75946 


25 


35 


.66371 


.88732 


1.1270 


.74799 


25 


36 


077 


710 


.1667 


927 


24 


36 


393 


784 


.1263 


780 


24 


37 


100 


761 


.1660 


908 


23 


37 


414 


836 


.1257 


760 


23 


38 


122 


811 


.1653 


889 


22 


38 


436 


888 


.1250 


741 


22 


39 


144 


862 


.1647 


870 


21 


39 


458 


940 


11243 


722 


21 


40 


.65166 


.85912 


1.1640 


.75851 


20 


40 


.66480 


.88992 


1.1237 


.74703 


20 


41 


188 


.85963 


.1633 


832 


19 


41 


501 


.89045 


.1230 


683 


19 


42 


210 


.86014 


.1626 


813 


18 


42 


523 


097 


.1224 


664 


18 


43 


232 


064 


.1619 


794 


17 


43 


545 


149 


.1217 


644 


17 


44 


254 


115 


.1612 


775 


16 


44 


566 


201 


.1211 


625 


16 


45 


.65276 


.86166 


1.1606 


.75756 


15 


45 


.66588 


.89253 


1.1204 


.74606 


15 


46 


298 


216 


.1599 


738 


14 


46 


610 


306 


.1197 


586 


14 


47 


320 


267 


.1592 


719 


13 


47 


632 


358 


.1191 


567 


13 


48 


342 


318 


.1585 


700 


12 


48 


653 


410 


.1184 


548 


12 


49 


364 


368 


.1578 


680 


11 


49 


675 


463 


.1178 


528 


11 


50 


.65386 


.86419 


1.1571 


.75661 


10 


50 


.66697 


.89515 


1.1171 


.74509 


10 


51 


408 


470 


.1565 


642 


9 


51 


718 


567 


.1165 


489 


9 


52 


430 


521 


.1558 


623 


8 


52 


740 


620 


.1158 


470 


8 


53 


452 


572 


.1551 


604 


7 


53 


762 


672 


.1152 


451 


7 


54 


474 


623 


.1544 


585 


6 


54 


783 


725 


.1145 


431 


6 


55 


.65496 


.86674 


1.1538 


.75566 


5 


55 


.66805 


.89777 


1.1139 


.74412 


5 


56 


518 


725 


.1531 


547 


4 


56' 


827 


830 


.1132 


392 


4 


57 


540 


776 


.1524 


528 


3 


57 


848 


883 


.1126 


373 


3 


58 


562 


827 


.1517 


509 


2 


58 


870 


935 


.1119 


353 


2 


59 


584 


878 


.1510 


490 


1 


59 


891 


.89988 


.1113 


334 


1 


60 


.65606 


.86929 


1.1504 


.75471 





60 


.66913 


.90040 


1.1106 


.74314 







Cos 


Ctn 


Tan 


Sin 


/ 




Cos 


Ctn 


Tan 


Sin 


/ 



49' 



48< 



II] 42° — Values of Trigonometric Functions — 43' 



43 



/ 


Sin 


Tan 


Ctn 


Cos 







.66913 


.90040 


1.1106 


.74314 


60 


1 


935 


093 


.1100 


295 


59 


2 


956 


146 


.1093 


276 


58 


3 


978 


199 


.1087 


256 


57 


4 


.66999 


251 


.1080 


237 


56 


5 


.67021 


.90304 


1.1074 


.74217 


55 


6 


043 


357 


.1067 


198 


54 


7 


064 


410 


.1061 


178 


53 


8 


086 


463 


„1054 


159 


52 


9 


107 


516 


.1048 


139 


51 


10 


.67129 


.90569 


1.1041 


.74120 


50 


11 


151 


621 


.1035 


100 


49 


12 


172 


674 


.1028 


080 


48 


13 


194 


727 


.1022 


061 


47 


14 


215 


781 


.1016 


041 


46 


15 


.67237 


.90834 


1.1009 


.74022 


45 


16 


258 


887 


.1003 


.74002 


44 


17 


280 


940 


.0996 


.73983 


43 


18 


301 


.90993 


.0990 


963 


42 


19 


323 


.91046 


.0983 


944 


41 


20 


.67344 


.91099 


1.0977 


.73924 


40 


21 


366 


153 


.0971 


904 


39 


22 


387 


206 


.0964 


885 


38' 


23 


409 


259 


.0958 


865 


37 


24 


430 


313 


.0951 


846 


36 


25 


.67452 


.91366 


1.0945 


.73826 


35 


26 


473 


419 


.0939 


806 


34 


27 


495 


473 


.0932 


787 


33 


28 


516 


526 


.0926 


767 


32 


29 


538 


580 


.0919 


747 


31 


30 


.67559 


.91633 


1.0913 


.73728 


30 


31 


580 


687 


.0907 


708 


29 


32 


602 


740 


.0900 


688 


28 


33 


623 


794 


.0894 


669 


27 


34 


645 


847 


.0888 


649 


26 


35 


.67666 


.91901 


1.0881 


.73629 


25 


36 


688 


.91955 


.0875 


610 


24 


37 


709 


.92008 


.0869 


590 


23 


38 


730 


062 


.0862 


570 


22 


39 


752 


116 


.0856 


551 


21 


40 


.67773 


.92170 


1.0850 


.73531 


20 


41 


795 


224 


.0843 


511 


19 


42 


816 


277 


.0837 


491 


18 


43 


837 


331 


.0831 


472 


17 


44 


859 


385 


.0824 


452 


16 


45 


.67880 


.92439 


1.0818 


.73432 


15 


46 


901 


493 


.0812 


413 


14 


47 


923 


547 


.0805 


393 


13 


48 


944 


601 


.0799 


373 


12 


49 


965 


655 


.0793 


353 


11 


50 


.67987 


.92709 


1.0786 


.73333 


10 


51 


.68008 


763 


.0780 


314 


9 


52 


029 


817 


.0774 


294 


8 


53 


051 


872 


:0768 


274 


7 


54 


072 


926 


.0761 


254 


6 


55 


.68093 


.92980 


1.0755 


.73234 


5 


56 


115 


.93034 


.0749 


215 


4 


57 


136 


088 


.0742 


195 


3 


58. 


157 


143 


.0736 


175 


2 


59 


179 


197 


.0730 


155 


1 


60 


.68200 


.93252 


1.0724 


.73135 







Cos 


Ctn 


Tan 


Sin 


/ 






Sin 


Tan 


Ctn 


Cos 




.68200 


.93252 


1.0724 


.73135 


60 


1 


221 


306 


.0717 


116 


59 


2 


242 


360 


.0711 


096 


58 


3 


264 


415 


.0705 


076 


57 


4 


285 


469 


.0699 


056 


56 


5 


.68306 


.93524 


1.0692 


.73036, 


55 


6 


327 


578 


.0686 


.73016 


54 


7 


349 


633 


.0680 


.72996 


53 


8 


370 


688 


.0674 


976 


52 


9 


391 


742 


.0668 


957 


51 


10 


.68412 


.93797 


1.0661 


.72937 


50 


11 


434 


852 


.0655 


917 


49 


12 


455 


906 


.0649 


897 


48 


13 


476 


.93961 


.0643 


877 


47 


14 


497 


.94016 


.0637 


857 


46 


15 


.68518 


.94071 


1.0630 


.72837 


45 


16 


539 


125 


.0624 


817 


44 


17 


561 


180 


.0618 


797 


43 


18 


582 


235 


.0612 


777 


42 


19 


603 


290 


.0606 


757 


41 


20 


.68624 


.94345 


1.0599 


.72737 


40 


21 


645 


400 


.0593 


717 


39 


22 


666 


455 


.0587 


697 


38 


23 


688 


510 


.0581 


677 


37 


24 


709 


565 


.0575 


657 


36 


25 


.68730 


.94620 


1.0569 


.72637 


35 


26 


751 


676 


.0562 


617 


34 


27 


772 


731 


.0556 


597 


33 


28 


793 


786 


.0550 


577 


32 


29 


814 


841 


.0544 


557 


31 


30 


.68835 


.94896 


1.0538 


.72537 


30 


31 


857 


.94952 


.0532 


517 


29 


32 


878 


.95007 


.0526 


497 


28 


33 


899 


062 


.0519 


477 


27 


34 


920 


118 


.0513 


457 


26 


35 


.68941 


.95173 


1.0507 


.72437 


25 


36 


962 


229 


.0501 


417 


24 


37 


.68983 


284 


.0495 


397 


23 


38 


.69004 


340 


.0489 


377 


22 


39 


025 


395 


.0483 


357 


21 


40 


.69046 


.95451 


1.0477 


.72337 


20 


41 


067 


506 


.0470 


317 


19 


42 


088 


562 


.0464 


297 


18 


43 


109 


618 


.0458 


277 


17 


44 


130 


673 


.0452 


257 


16 


45 


.69151 


.95729 


1.0446 


.72236 


15 


46 


172 


785 


.0440 


216 


14 


47 


193 


841 


.0434 


196 


13 


48 


214 


897 


.0428 


176 


12 


49 


235 


.95952 


.0422 


156 


11 


50 


.69256 


.96008 


1.0416 


.72136 


10 


51 


277 


064 


.0410 


116 


9 


52 


298 


120 


.0404 


095 


8 


53 


319 


176 


.0398 


075 


7 


54 


340 


232 


.0392 


055 


6 


55 


.69361 


.96288 


1.0385 


.72035 


5 


56 


382 


344 


.0379 


.72015 


4 


57 


403 


400 


.0373 


.71995 


3 


58 


424 


457 


.0367 


974 


2 


59 


445 


513 


.0361 


954 


1 


60 


.69466 


.96569 


1.0355 


.71934 







Cos 


Ctn 


Tan 


Sin 


1 



47' 



46' 



44 



44° — Values of Trigonometric Functions 



PI 



/ 


Sin 


Tan 


Ctn 


Cos 







.69466 


.96569 


1.0355 


.71934 


60 


1 


487 


625 


.0349 


914 


59 


2 


508 


681 


.0343 


894 


58 


3 


529 


738 


.0337 


873 


57 


4 


549 


794 


.0331 


853 


56 


5 


.69570 


.96850 


1.0325 


.71833 


55 


6 


591 


907 


.0319 


813 


54 


7 


612 


.96963 


.0313 


792 


53 


8 


633 


.97020 


.0307 


772 


52 


9 


654 


076 


.0301 


752 


51 


10 


.69675 


.97133 


1.0295 


.71732 


50 


11 


696 


189 


.0289 


711 


49 


12 


717 


246 


.0283 


691 


48 


13 


737 


302 


.0277 


671 


47 


14 


758 


359 


.0271 


650 


46 


15 


.69779 


.97416 


1.0265 


.71630 


45 


16 


800 


472 


.0259 


610 


44 


17 


821 


529 


.0253 


590 


43 


18 


842 


586 


.0247 


569 


42 


19 


862 


643 


.0241 


549 


41 


20 


.69883 


.97700 


1.0235 


.71529 


40 


21 


904 


756 


.0230 


508 


39 


22 


925 


813 


.0224 


488 


38 


23 


946 


870 


.0218 


468 


37 


24 


966 


927 


.0212 


447 


36 


25 


.69987 


.97984 


1.0206 


.71427 


35 


26 


.70008 


.98041 


.0200 


407 


34 


27 


029 


098 


.0194 


386 


33 


28 


049 


155 


.0188 


366 


32 


29 


070 


213 


.0182 


345 


31 


30 


.70091 


.98270 


1.0176 


.71325 


30 


31 


112 


327 


.0170 


305 


29 


32 


132 


384 


.0164 


284 


28 


33 


153 


441 


.0158 


264 


27 


34 


174 


499 


.0152 


243 


26 


35 


.70195 


.98556 


1.0147 


.71223 


25 


36 


215 


613 


.0141 


203 


24 


37 


236 


671 


.0135 


182 


23 


38 


257 


728 


.0129 


162 


22 


39 


277 


786 


.0123 


141 


21 


40 


.70298 


.98843 


1.0117 


.71121 


20 


41 


319 


901 


.0111 


100 


19 


42 


339 


.98958 


.0105 


080 


18 


43 


360 


.99016 


.0099 


059 


17 


44 


381 


073 


.0094 


039 


16 


45 


.70401 


.99131 


1.0088 


.71019 


15 


46 


422 


189 


.0082 


.70998 


14 


47 


443 


247 


.0076 


978 


13 


48 


463 


304 


.0070 


957 


12 


49 


484 


362 


.0064 


937 


11 


50 


.70505 


.99420 


1.0058 


.70916 


10 


51 


525 


478 


.0052 


896 


9 


52 


546 


536 


.0047 


875 


8 


53 


567 


594 


.0041 


855 


7 


54 


587 


652 


.0035 


834 


6 


55 


.70608 


.99710 


1.0029 


.70813 


5 


56 


628 


768 


.0023 


793 


4 


57 


649 


826 


.0017 


*772 


3 


58 


670 


884 


.0012 


752 


2 


59 


690 


.99942 


.0006 


731 


1 


60 


.70711 


1.0000 


1.0000 


.70711 







Cos 


Ctn 


Tan 


Sin 


/ 



45' 



TABLE in 
COMMON LOGARITHMS 

OF THE 

TRIGONOMETRIC FUNCTIONS 

FROM 

0° TO 90° AT INTERVALS OF ONE MINUTE 

TO 

FIVE DECIMAL PLACES 

From each logarithm given, subtract 10 



Table Ilia — Auxiliary Table of S and T for A in Minutes 

S = log sin A — log A' and T = log tan A — log A f 



A' 


S+10 


0' - 13' 

14' - 42' 

43' - 58' 

59' - 71' 

72' - 81' 

82' - 91' 

92' - 99' 

100' - 107' 

108' - 115' 

116' - 121' 

122' - 128' 

129' - 134' 

135' - 140' 

141' - 146' 

147' - 151' 

152' - 157' 

158' - 162' 

163' - 167' 

168' - 171' 

172' - 176' 

177' - 181' 


6.46373 
72 
71 

6.46370 
69 
68 

6.46367 
66 
65 

6.46364 
63 
62 

6.46361 
60 
59 

6.46358 
57 
56 

6.46355 
54 
53 



A' 


T+10 


0' - 


26' 


6.46373 


27' - 


39' 


74 


40' - 


48' 


75 


49' - 


56' 


6.46376 


57' - 


63' 


77 


64' - 


69' 


78 


70' - 


74' 


6.46379 


75' - 


80' 


80 


81' - 


85' 


81 


86' - 


89' 


6.46382 


90' - 


94' 


83 


95' - 


98' 


84 


99' - 


102' 


6.46385 


103' - 


106' 


86 


107' - 


110' 


87 


111' - 


113' 


6.46388 


114' - 


117' 


89 


118' - 


120' 


90 


121' - 


124' 


6.46391 


125' - 


127' 


92 


128' - 


130' 


93 



A' 


T+10 


131' 


- 133' 


6.46394 


134' 


- 136' 


95 


137' 


- 139' 


96 


140' 


- 142' 


6.46397 


143' 


- 145' 


98 


146' 


- 148' 


99 


149' 


- 150' 


6.46400 


151' 


- 153' 


01 


154' 


- 156' 


02 


157' 


- 158' 


6.46403 


159' 


- 161' 


04 


162' 


- 163' 


05 


164' 


- 166' 


6.46406 


167' 


- 168' 


07 


169' 


- 171' 


08 


172' 


- 173' 


6.46409 


174' 


- 175' 


10 


176' 


- 178' 


11 


179' 


- 180' 


6.46412 


181' 


- 182' 


13 


183' 


- 184' 


14 



For small angles: log sin A = log A' -f- S and log tan A = log A f + T. 
For angles near 90°: log cos A = log (90° - A)' + S, log ctn A = log (90° - AY 
+ T where A' = number of minutes in A, and (90° — A)' = number of minutes 
in 90° - A. 

45 



46 



0° — Logarithms of Trigonometric Functions 



[HI 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



6.46 373 
6.76 476 
6.94 085 
7.06 579 

7.16 270 
7.24 188 
7.30 882 
7.36 682 
7.41 797 

7.46 373 
7.50 512 
7.54 291 

7.57 767 
7.60 985 

7.63 982 
7.66 784 
7.69 417 
7.71 900 

7.74 248 

7.76 475 

7.78 594 
7.80 615 
7.82 545 
7.84 393 

7.86 166 

7.87 870 
7.89 509 

7.91 088 

7.92 612 

7.94 084 

7.95 508 

7.96 887 

7.98 223 

7.99 520 

8.00 779 

8.02 002 

8.03 192 

8.04 350 

8.05 478 

8.06 578 

8.07 650 

8.08 696 

8.09 718 

8.10 717 



11693 

12 647 

13 581 

14 495 

15 391 

16 268 

17 128 

17 971 

18 798 

19 610 

20 407 

21 189 
21958 

22 713 

23 456 

24 186 



LCos 



30103 

17609 

12494 

9691 

7918 
6694 
5800 
5115 
4576 

4139 
3779 
3476 
3218 
2997 
2802 
2633 
2483 
2348 
2227 

2119 
2021 
930 
848 
773 

704 
639 
579 
524 
472 
424 
379 
336 
297 
259 

223 

190 
158 
128 
100 
072 
046 
022 
999 
976 
954 
934 
914 
896 
877 
S60 
843 
827 
812 
797 
782 
769 
755 
743 
730 



LTan 



6.46 373 
6.76 476 
6.94 085 
7.06 579 

7.16 270 
7.24 188 
7.30 882 
7.36 682 
7.41 797 

7.46 373 
7.50 512 
7.54 291 

7.57 767 
7.60 986 

7.63 982 
7.66 785 
7.69 418 
7.71 900 

7.74 248 

7.76 476 

7.78 595 
7.80 615 
7.82 546 
7.84 394 

7.86 167 

7.87 871 
7.89 510 

7.91 089 

7.92 613 

7.94 086 

7.95 510 

7.96 889 

7.98 225 

7.99 522 

8.00 781 

8.02 004 

8.03 194 

8.04 353 

8.05 481 

8.06 581 

8.07 653 

8.08 700 

8.09 722 

8.10 720 

8.11 696 

8.12 651 

8.13 585 

8.14 500 

8.15 395 

8.16 273 

8.17 133 

8.17 976 

8.18 804 

8.19 616 

8.20 413 

8.21 195 

8.21 964 

8.22 720 

8.23 462 

8.24 192 



L Ctn c d 



cd 



30103 

17609 

12494 

9691 

7918 
6694 
5800 
5115 
4576 

4139 
3779 
3476 
3219 
2996 

2803 
2633 

2482 
2348 
2228 

2119 
2020 
931 
848 
773 
704 
639 
579 
524 
473 
424 
379 
336 
297 
259 
223 
190 
159 
128 
100 
072 
047 
022 
998 
976 
955 
934 
915 
895 
878 
860 
843 
828 
812 
797 
782 
769 
756 
742 
730 



LCtn 



13.53 627 
13.23 524 

13.05 915 

12.93 421 

12.83 730 

12.75 812 
12.69 118 
12.63 318 
12.58 203 

12.53 627 
12.49 488 
12.45 709 
12.42 233 
12.39 014 

12.36 018 
12.33 215 
12.30 582 
12.28 100 
12.25 752 

12.23 524 
12.21 405 
12.19 385 
12.17 454 
12.15 606 

12.13 833 
12.12 129 
12.10 490 
12.08 911 
12.07 387 

12.05 914 
12.04 490 
12.03 111 
12.01 775 
12.00 478 

11.99 219 
11.97 996 
11.96 806 
11.95 647 

11.94 519 
11.93 419 
11.92 347 
11.91 300 
11.90 278 
11.89 280 
11.88 304 
11.87 349 
11.86 415 
11.85 500 

11.84 605 

11.83 727 
11.82 867 
11.82 024 
11.81 196 
11.80 384 

11.79 587 
11.78 805 
11.78 036 
11.77 280 

11.76 538 
11.75 808 



LTan 



LCos 



10.00 000 
10.00 000 
10.00 000 
10.00 000 
10.00 000 



10.00 
10.00 
10.00 
10.00 
10.00 
10.00 
10.00 
10.00 
10.00 
10.00 



000 
000 
000 
000 
000 
000 
000 
000 
000 
000 



10.00 000 

10.00 000 

9.99 999 

9.99 999 

9.99 999 

9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 999 
9.99 998 

9.99 998 
9.99 998 
9.99 998 
9.99 998 
9.99 998 

9.99 998 
9.99 998 
9.99 997 
9.99 997 
9.99 997 
9.99 997 
9.99 997 
9.99 997 
9.99 997 
9.99 996 

9.99 996 
9.99 996 
9.99 996 
9.99 996 
9.99 996 
9.99 995 
9.99 995 
9.99 995 
9.99 995 
9.99 995 
9.99 994 
9.99 994 
9.99 994 
9.99 994 
9.99 994 

9.99 993 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 

42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 
25 
24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 





to 



© 



o P*^ 

W B 2 

o " 3 

CO © «2 

i-H *>• -fr 3 

bJDQO c3 

O +> fcfl 

go u H 

O 03 © 

bfi © % 

i t-4 03 

* ® § 

•5 <■£ Ss 

02 O ^3 

«4-t co ?h 

© 2 

3 Pi 03 

^3 o3^ 



co 



& ° 

u 

o 



© 

-a 

PI 

© 



<D © 
bO P* 
rt CO 

*"1 

A Pi 

*.2 

CD O 

•a & 

2 p! 
co .pj 

£ o 
© o 

s e 

CO ^ 

a a 

<N o 

r d © 

P! Si 

o > 
^- <p 

*& _r 
© T3 
-+? © 

C3 f-t 

18 '3 

js 8f 

C3 ^^3 

PU O 






oq 



© 

03 

o © 

A 03 



89° — Logarithms of Trigonometric Functions 



Ill] 1° — Logarithms of Trigonometric Functions 



47 



o 

i 

2 
3 
4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 
17 
18 
19 
20 
21 
22 
23 
24 

25 

26 
27 
28 
29 
30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 

42 
43 

44 
45 
46 

47 
48 
49 

50 

51 

52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



8.24 186 

8.24 903 

8.25 609 

8.26 304 

8.26 988 

8.27 661 

8.28 324 

8.28 977 

8.29 621 

8.30 255 

8.30 879 

8.31 495 

8.32 103 

8.32 702 

8.33 292 

8.33 875 

8.34 450 

8.35 018 

8.35 578 

8.36 131 



8. 

8. 
8. 
8, 
8. 

8. 
8, 
8, 
8, 
8, 
8, 
8, 
8, 
8 
8 
8 
8 
8 
8 
8 

8.46 366 

8.46 799 

8.47 226 

8.47 650 

8.48 069 
8.48 485 

8.48 896 

8.49 304 

8.49 708 

8.50 108 



36 678 

37 217 

37 750 

38 276 

38 796 

39 310 

39 818 

40 320 
40 816 
41307 
.41 792 
.42 272 
.42 746 
.43 216 
.43 680 
.44 139 
.44 594 
.45 044 
.45 489 
.45 930 



50 504 
50 897 
51287 
51673 
52 055 
52 434 

52 810 

53 183 
53 552 

53 919 

54 282 



717 

706 
695 
684 
673 
663 
653 
644 
634 
624 

616 
608 
599 
590 
583 

575 
568 
560 
553 
547 
539 
533 
526 
520 
514 

508 
502 
496 
491 

485 

480 
474 
470 
464 
459 
455 
450 
445 
441 
436 
433 
427 
424 
419 
416 
411 
408 
404 
400 
396 

393 
390 
386 
382 
379 
376 
373 
369 
367 
363 



LTan 



24 192 

24 910 

25 616 

26 312 

26 996 

27 669 

28 332 

28 986 

29 629 

30 263 
30 888 
31505 
32 112 

32 711 

33 302 

33 886 

34 461 

35 029 

35 590 

36 143 

36 689 

37 229 

37 762 

38 289 

38 809 

39 323 

39 832 

40 334 
40 830 
41321 

41807 
42 287 

42 762 

43 232 

43 696 

44 156 

44 611 

45 061 
45 507 

45 948 

46 385 

46 817 

47 245 

47 669 

48 089 
48 505 

48 917 

49 325 
49 729 
,50 130 
.50 527 
.50 920 
.51 310 
.51 696 
.52 079 
.52 459 
.52 835 
.53 208 
.53 578 
.53 945 
.54 308 



c d L Ctn L Cos 



718 
706 
696 
684 
673 
663 
654 
643 
634 
625 

617 
607 
599 
591 
584 
575 
568 
561 
553 
546 

540 
533 
527 
520 
514 

509 
502 
496 
491 
486 

480 
475 

470 
464 
460 

455 

450 
446 
441 
437 
432 
428 
424 
420 
416 
412 
408 
404 
401 
397 
393 
390 
386 
383 
380 

376 
373 
370 
367 
363 



L Cos d L Ctn I c d L Tan L Sin 



11.75 808 
11.75 090 
11.74 384 
11.73 688 
11.73 004 

11.72 331 
11.71 668 
11.71 014 
11.70 371 
11.69 737 
11.69 112 
11.68 495 
11.67 888 
11.67 289 
11.66 698 
11.66 114 
11.65 539 
11.64 971 
11.64 410 
11.63 857 
11.63 311 
11.62 771 
11.62 238 
11.61711 
11.61 191 

11.60 677 
11.60 168 
11.59 666 
11.59 170 
11.58 679 
11.58 193 
11.57 713 
11.57 238 
11.56 768 
11.56 304 
11.55 844 
11.55 389 
11.54 939 
11.54 493 
11.54 052 

11.53 615 
11.53 183 
11.52 755 
11.52 331 
11.51911 
11.51 495 
11.51 083 
11.50 675 
11.50 271 
11.49 870 

11.49 473 
11.49 080 
11.48 690 
11.48 304 
11.47 921 
11.47 541 
11.47 165 
11.46 792 
11.46 422 
11.46 055 
11.45 692 



9.99 993 
9.99 993 
9.99 993 
9.99 993 
9.99 992 
9.99 992 
9.99 992 
9.99 992 
9.99 992 
9.99 991 
9.99 991 
9.99 991 
9.99 990 
9.99 990 
9.99 990 
9.99 990 
9.99 989 
9.99 989 
9.99 989 
9.99 989 
9.99 988 
9.99 988 
9.99 988 
9.99 987 
9.99 987 
9.99 987 
9.99 986 
9.99 986 
9.99 986 
9.99 985 
9.99 985 
9.99 985 
9.99 984 
9.99 984 
9.99 984 

9.99 983 
9.99 983 
9.99 983 
9.99 982 
9.99 982 
9.99 982 
9.99 981 
9.99 981 
9.99 981 
9.99 980 
9.99 980 
9.99 979 
9.99 979 
9.99 979 
9.99 978 
9.99 978 
9.99 977 
9.99 977 
9.99 977 
9.99 976 

9.99 976 
9.99 975 
9.99 975 
9.99 974 
9.99 974 
9.99 974 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 

1 




Prop. Pts. 



710 690 

142 138 

213 207 

284 276 

355 345 

426 414 

497 483 

568 552 



670 650 

134 130 

201 195 

268 260 

335 325 

402 390 

469 455 

536 520 



639 621 603 585 



630 620 

126 124 

189 186 

252 248 

315 310 

378 372 

441 434 

504 496 



610 600 

122 120 

183 180 

244 240 

305 300 

366 360 

427 420 

488 480 



567 558 549 540 



590 580 

118 116 

177 174 

236 232 

295 290 

354 348 

413 406 

472 464 

531 522 

550 540 

110 108 

165 162 

220 216 

275 270 

330 324 

385 378 

440 432 

495 486 

510 500 



2 


102 


100 


3 


153 


150 


4 


204 


200 


5 


255 


250 


6 


306 


300 


7 


357 


350 


8 


408 


400 


9 


459 


450 



570 560 

114 112 

171 168 

228 224 

285 280 

342 336 

399 392 

456 448 

513 504 



530 520 

106 104 

159 156 

212 208 

265 260 

318 312 

371 364 

424 416 

477 468 

490 480 

98 96 

147 144 

196 192 

245 240 

294 288 

343 336 

392 384 

441 432 



470 460 

94 92 

141 138 

188 184 

235 230 

282 276 

329 322 

376 368 

423 414 405 396 



450 440 

90 88 

135 132 

180 176 

225 220 

270 264 

315 308 

360 352 



430 420 

86 84 

129 126 

172 168 

215 210 

258 252 

301 294 

344 336 

387 378 



390 380 

78 76 

117 114 

156 152 

195 190 

234 228 

273 266 

312 304 

351 342 



410 400 

82 80 

123 120 

164 160 

205 200 

246 240 

287 280 

328 320 

369 360 

370 360 

74 72 

111 108 

148 144 

185 180 

222 216 

259 252 

296 288 

333 324 



Prop. Pts. 



88° — Logarithms of Trigonometric Functions 



48 



Logarithms of Trigonometric Functions 



[III 



o 

1 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 
40 
41 
42 
43 
44 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



LSin 



8.54 282 
8.54 642 

8.54 999 

8.55 354 

8.55 705 

8.56 054 
8.56 400 

8.56 743 

8.57 084 
8.57 421 

8.57 757 

8.58 089 
8.58 419 

8.58 747 

8.59 072 
8.59 395 

8.59 715 

8.60 033 
8.60 349 
8.60 662 

8.60 973 

8.61 282 
8.61 589 

8.61 894 

8.62 196 



.62 497 
.62 795 
.63 091 
.63 385 
.63 678 

.63 968 
.64 256 
.64 543 
.64 827 
.65 110 



8.65 391 
8.65 670 

8.65 947 

8.66 223 
8.66 497 

8.66 769 

8.67 039 
8.67 308 
8.67 575 

8.67 841 

8.68 104 
8.68 367 
8.68 627 

8.68 886 

8.69 144 



69 400 
69 654 

69 907 

70 159 
70 409 
70 658 

70 905 
71151 
71395 

71 638 
71880 



LCos 



360 
357 
355 
351 
349 

346 
343 
341 
337 
336 
332 
330 
328 
325 
323 

320 
318 
316 
313 
311 

309 
307 
305 
302 
301 
298 
296 
294 
293 
290 
288 
287 
284 
283 
281 

279 
277 
276 
274 
272 

270 
269 
267 
266 
263 
263 
260 
259 
258 
256 
254 
253 
252 
250 
249 

247 
246 
244 
243 
242 



L Tan c d L Ctn L Cos 



8.54 308 

8.54 669 

8.55 027 
8.55 382 

8.55 734 

8.56 083 
8.56 429 

8.56 773 

8.57 114 
8.57 452 

8.57 788 

8.58 121 
8.58 451 

8.58 779 

8.59 105 

8.59 428 

8.59 749 

8.60 068 
8.60 384 

8.60 698 

8.61 009 
8.61319 
8.61 626 

8.61 931 

8.62 234 

8.62 535 

8.62 834 

8.63 131 
8.63 426 

8.63 718 

8.64 009 
8.64 298 
8.64 585 

8.64 870 

8.65 154 
8.65 435 
8.65 715 

8.65 993 

8.66 269 
8.66 543 

8.66 816 

8.67 087 
8.67 356 
8.67 624 

8.67 890 

8.68 154 
8.68 417 
8.68 678 

8.68 938 

8.69 196 
8.69 453 
8.69 708 

8.69 962 

8.70 214 
8.70 465 
8.70 714 

8.70 962 

8.71 208 
8.71 453 
8.71 697 
8.71 940 



LCtn cd 



361 
358 
355 
352 
349 
346 
344 
341 
338 
336 
333 
330 
328 
326 
323 
321 
319 
316 
314 
311 

310 
307 
305 
303 
301 
299 
297 
295 
292 
291 

289 
287 
285 
284 
281 

280 
278 
276 
274 
273 
271 
269 
268 
266 
264 

263 
261 
260 
258 
257 
255 
254 
252 
251 
249 
248 
246 
245 
244 
243 



11.45 692 
11.45 331 
11.44 973 
11.44 618 
11.44 266 

11.43 917 
11.43 571 
11.43 227 
11.42 886 
11.42 548 
11.42 212 
11.41879 
11.41549 
11.41 221 
11.40 895 
11.40 572 
11.40 251 
11.39 932 
11.39 616 
11.39 302 

11.38 991 
11.38 681 
11.38 374 
11.38 069 
11.37 766 
11.37 465 
11.37 166 
11.36 869 
11.36 574 
11.36 282 

11.35 991 
11.35 702 
11.35 415 
11.35 130 
11.34 846 
11.34 565 
11.34 285 
11.34 007 
11.33 731 
11.33 457 
11.33 184 
11.32 913 
11.32 644 
11.32 376 
11.32 110 

11.31 846 
11.31583 
11.31322 
11.31 062 
11.30 804 

11.30 547 
11.30 292 
11.30 038 
11.29 786 
11.29 535 
11.29 28,6 
11.29 038 
11.28 792 
11.28 547 
11.28 303 
11.28 060 



LTan 



9.99 974 
9.99 973 
9.99 973 
9.99 972 
9.99 972 
9.99 971 
9.99 971 
9.99 970 
9.99 970 
9.99 969 
9.99 969 
9.99 968 
9.99 968 
9.99 967 
9.99 967 
9.99 967 
9.99 966 
9.99 966 
9.99 965 
9.99 964 

9.99 964 
9.99 963 
9.99 963 
9.99 962 
9.99 962 
9.99 961 
9.99 961 
9.99 960 
9.99 960 
9.99 959 
9.99 959 
9.99 958 
9.99 958 
9.99 957 
9.99 956 
9.99 956 
9.99 955 
9.99 955 
9.99 954 
9.99 954 
9.99 953 
9.99 952 
9.99 952 
9.99 951 
9.99 951 
9.99 950 
9.99 949 
9.99 949 
9.99 948 
9.99 948 
9.99 947 
9.99 946 
9.99 946 
9.99 945 
9.99 944 
9.99 944 
9.99 943 
9.99 942 
9.99 942 
9.99 941 
9.99 940 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 
50 
49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 
11 
10 
9 
8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 



360 

72 
108 
144 
180 
216 
252 
288 
324 

345 

69.0 
103.5 
138.0 
172.5 
207.0 
241.5 
276.0 
310.5 



330 

66 

99 
132 
165 
198 
231 
264 
297 

315 

63.0 
94.5 
126.0 
157.5 
189.0 
220.5 
252.0 
283.5 

300 

60 

90 
120 
150 
180 
210 
240 
270 

285 

57.0 
85.5 
114.0 
142.5 
171.0 
199.5 
228.0 
256.5 

270 

54 

81 
108 
135 
162 
189 
216 
243 

255 

51.0 

76.5 
102.0 
127.5 
153.0 
178.5 
204.0 
229.5 



355 

71.0 

106.5 
142.0 
177.5 
213.0 
248.5 
284.0 
319.5 

340 

68 
102 
136 
170 
204 
238 
272 
306 

325 

65.0 

97.5 

130.0 
162.5 
195.0 
227.5 
260.0 
292.5 

310 

62 

93 
124 
155 
186 
217 
248 
279 



295 

59.0 

88.5 
118.0 
147.5 
177.0 
206.5 
236.0 
265.5 

280 
56 

84 
112 
140 
168 
196 
224 
252 

265 

53.0 

79.5 
106.0 
132.5 
159.0 
185.5 
212.0 
238.5 



250 

50 
75 

100 
125 
150 
175 
200 
225 



350 

70 
105 
140 
175 
210 
245 
280 
315 

335 

67.0 
100.5 
134.0 
167.5 
201.0 
234.5 
268.0 
301.5 



320 

64 

96 
128 
160 
192 
224 
256 
288 

305 

61.0 
91.5 
122.0 
152.5 
183.0 
213.5 
244.0 
274.5 

290 

58 

87 
116 
145 
174 
203 
232 
261 



275 

55.0 
82.5 
110.0 
137.5 
165.0 
192.5 
220.0 
247.5 

260 

52 

78 
104 
130 
156 
182 
208 
234 



245 

49.0 
73.5 
98.0 
122.5 
147.0 
171.5 
196.0 
220.5 



Prop. Pts. 



87° — Logarithms of Trigonometric Functions 



Ill] 



3° — Logarithms of Trigonometric Functions 



49 



LSin 



LTan 



cd 



LCtn 



LCos 



Prop. Pts. 





1 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 
30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



8.71 880 

8.72 120 
8.72 359 
8.72 597 

8.72 834 

8.73 069 
8.73 303 
8.73 535 
8.73 767 

8.73 997 

8.74 226 
8.74 454 
8.74 680 

8.74 906 

8.75 130 
8.75 353 
8.75 575 

8.75 795 

8.76 015 
8.76 234 

8.76 451 
8.76 667 

8.76 883 

8.77 097 
8.77 310 

8.77 522 
8.77 733 

8.77 943 

8.78 152 
8.78 360 

8.78 568 
8.78 774 

8.78 979 

8.79 183 
8.79 386 



79 588 
79 789 

79 990 

80 189 
80 388 

80 585 
80 782 
.80 978 
.81 173 
81367 

81560 

81752 
81944 
82 134 
82 324 

82 513 
82 701 

82 888 

83 075 
83 261 

83 446 
83 630 
83 813 

83 996 

84 177 
84 358 



240 
239 
238 
237 
235 

234 
232 
232 
230 
229 
228 
226 
226 
224 
223 
222 
220 
220 
219 
217 
216 
216 
214 
213 
212 
211 
210 
209 
208 
208 

206 
205 
204 
203 
202 

201 

201 

99 

99 

97 

97 
96 
95 
94 
93 

92 
92 
90 
90 

89 

88 
87 
87 
86 
85 

84 
83 

83 

81 
81 



71940 
72 181 
72 420 
72 659 

72 896 

73 132 
73 366 
73 600 

73 832 

74 063 
74 292 
74 521 
74 748 

74 974 

75 199 

75 423 
75 645 

75 867 

76 087 
76 306 

76 525 

76 742 

76 958 

77 173 

77 387 

77 600 

77 811 

78 022 

78 232 
78 441 

78 649 

78 855 

79 061 
79 266 
79 470 

79 673 

79 875 

80 076 
80 277 
80 476 
80 674 

80 872 

81 068 
81 264 
81 459 

81 653 
,81 846 
,82 038 
,82 230 
,82 420 

82 610 
,82 799 
,82 987 
,83 175 
,83 361 

,83 547 
,83 732 
,83 916 
,84 100 

,84 282 

84 464 



241 
239 
239 
237 
236 

234 
234 
232 
231 
229 

229 
227 
226 
225 
224 

222 

222 
220 
219 
219 

217 
216 
215 
214 
213 

211 
211 

210 
209 
208 

206 
206 
205 
204 
203 
202 
201 
201 
99 
98 

98 
96 
96 
95 
94 

93 

92 
92 
90 
90 

89 



1.28 060 
1.27 819 
1.27 580 
1.27 341 
1.27 104 

1.26 868 
1.26 634 
1.26 400 
1.26 168 
1.25 937 
1.25 708 
1.25 479 
1.25 252 
1.25 026 
1.24 801 

1.24 577 
1.24 355 
1.24 133 
1.23 913 
1.23 694 

1.23 475 
1.23 258 
1.23 042 
1.22 827 
1.22 613 
1.22 400 
1.22 189 
1.21 978 
1.21 768 
1.21 559 

1.21 351 
1.21 145 
1.20 939 
1.20 734 
1.20 530 

1.20 327 
1.20 125 
1.19 924 
1.19 723 
1.19 524 

1.19 326 
1.19 128 
1.18 932 
1.18 736 
1.18 541 

1.18 347 
1.18 154 
1.17 962 
1.17 770 
1.17 580 
1.17 390 
1,17 201 
1.17 013 
1.16 825 
1.16 639 

1.16 453 
1.16 268 
1.16 084 
1.15 900 
1.15 718 

1.15 536 



9.99 940 
9.99 940 
9.99 939 
9.99 938 
9.99 938 

9.99 937 
9.99 936 
9.99 936 
9.99 935 
9.99 934 

9.99 934 
9.99 933 
9.99 932 
9.99 932 
9.99 931 

9.99 930 
9.99 929 
9.99 929 
9.99 928 
9.99 927 

9.99 926 
9.99 926 
9.99 925 
9.99 924 
9.99 923 

9.99 923 
9.99 922 
9.99 921 
9.99 920 
9.99 920 

9.99 919 
9.99 918 
9.99 917 
9.99 917 
9.99 916 

9.99 915 
9.99 914 
9.99 913 
9.99 913 
9.99 912 

9.99 911 
9.99 910 
9.99 909 
9.99 909 
9.99 908 

9.99 907 
9.99 906 
9.99 905 
9.99 904 
9.99 904 

9.99 903 
9.99 902 
9.99 901 
9.99 900 
9.99 899 

9.99 898 
9.99 898 
9.99 897 
9.99 896 
9.99 895 
9.99 894 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 



240 

48 

72 

96 
120 
144 
168 
192 
216 

225 

45.0 

67.5 

90.0 

112.5 

135.0 

157.5 

180.0 

202.5 

213 

42.6 

63.9 

85.2 

106.5 

127.8 

149.1 

170.4 

191.7 

206 

41.2 

61.8 

82.4 

103.0 

123.6 

144.2 

164.8 

185.4 

199 

39.8 

59.7 

79.6 

99.5 

119.4 

139.3 

159.2 

179.1 

193 

38.6 

57.9 

77.2 

96.5 

115.8 

135.1 

154.4 

173.7 

188 

37.6 

56.4 

75.2 

94.0 

112.8 

131.6 

150.4 

169.2 

183 

36.6 

54.9 

73.2 

91.5 

109.8 

128.1 

146.4 

164.7 



235 

47.0 
70.5 
94.0 
117.5 
141.0 
164.5 
188.0 
211.5 

220 

44.0 
66.0 
88.0 
110.0 
132.0 
154.0 
176.0 
198.0 



211 

42.2 

63.3 

84.4 

105.5 

126.6 

147.7 

168.8 

189.9 

203 

40.6 

60.9 

81.2 

101.5 

121.8 

142.1 

162.4 

182.7 

197 

39.4 

59.1 

78.8 

98.5 

118.2 

137.9 

157.6 

177.3 

192 

38.4 

57.6 

76.8 

96.0 

115.2 

134.4 

153.6 

172.8 



186 

37.2 

55.8 

74.4 

93.0 

111.6 

130.2 

148.8 

167.4 

182 

36.4 

54.6 

72.8 

91.0 

109.2 

127.4 

145.6 

163.8 



230 

46 

69 

92 

115 

138 
161 

184 
207 

215 

43.0 
64.5 
86.0 
107.5 
129.0 
150.5 
172.0 
193.5 

208 

41.6 
62.4 
83.2 
104.0 
124.8 
145.6 
166.4 
187.2 

201 

40.2 

60.3 

80.4 

100.5 

120.6 

140.7 

160.8 

180.9 



195 

39.0 

58.5 

78.0 

97.5 

117.0 

136.5 

156.0 

175.5 

190 

38.0 

57.0 

76.0 

95.0 

114.0 

133.0 

152.0 

171.0 

184 

36.8 

55.2 

73.6 

92.0 

110.4 

128.8 

147.2 

165.6 

181 

36.2 

54.3 

72.4 

90.5 

108.6 

126.7 

144.8 

162.9 



LCos 



L Ctn c d 



LTan I LSin 



Prop. Pts. 



86° — Logarithms of Trigonometric Functions 



50 



4° — Logarithms of Trigonometric Functions 



[HI 



o 

i 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



8.84 358 
8.84 539 
8.84 718 

8.84 897 

8.85 075 
8.85 252 
8.85 429 
8.85 605 
8.85 780 

8.85 955 

8.86 128 
8.86 301 
8.86 474 
8.86 645 
8.86 816 

8.86 987 

8.87 156 
8.87 325 
8.87 494 
8.87 661 
8.87 829 

8.87 995 

8.88 161 
8.88 326 
8.88 490 

8.88 654 
8.88 817 

8.88 980 

8.89 142 
8.89 304 



89 464 
89 625 
89 784 

89 943 
90102 

90 260 
90 417 
90 574 
90 730 
90 885 



8.91040 
8.91 195 
8.91 349 
8.91 502 
8.91 655 

8.91 807 

8.91 959 

8.92 110 
8.92 261 
8.92 411 

8.92 561 
8.92 710 

8.92 859 

8.93 007 
8.93 154 

8.93 301 
8.93 448 
8.93 594 
8.93 740 

8.93 885 

8.94 030 



LCos 



181 
179 
179 

178 
177 

177 
176 
175 
175 
173 

173 
173 
171 
171 
171 

169 
169 
169 
167 
168 

166 
166 
165 
164 
164 

163 
163 
162 
162 
160 
161 
159 
159 
159 
158 

157 
157 
156 
155 
155 

155 
154 
153 
153 
152 

152 
151 
151 
150 
150 

149 
149 
148 
147 
147 

147 
146 
146 
145 
145 



L Tan c d 



84 464 
84 646 

84 826 

85 006 
85 185 

85 363 
85 540 

85 717 

85 893 

86 069 

86 243 
86 417 
86 591 
86 763 

86 935 

87 106 

87 277 
87 447 
87 616 
87 785 

87 953 

88 120 

88 287 
88 453 
88 618 

88 783 

88 948 

89 111 
89 274 
89 437 
89 598 
89 760 

89 920 

90 080 
90 240 

90 399 
90 557 
90 715 

90 872 
91029 

91 185 

91340 
91495 
91650 
91803 

91957 

92 110 
92 262 
92 414 
92 565 

92 716 

92 866 
,93 016 
,93 165 
.93 313 
.93 462 
.93 609 

93 756 
.93 903 

94 049 

94 195 



182 
180 
180 
179 

178 

177 
177 
176 
176 

174 

174 
174 
172 
172 
171 
171 
170 
169 
169 
168 

167 
167 
166 
165 
165 

165 
163 
163 
163 
161 
162 
160 
160 
160 
159 

158 
158 
157 
157 
156 

155 
155 
155 
153 
154 

153 
152 
152 
151 
151 
150 
150 
149 
148 
149 

147 
147 
147 
146 
146 



LCtn 



L Ctn c d L Tan 



11.15 536 
11.15 354 
11.15 174 
11.14 994 
11.14 815 

11.14 637 
11.14 460 
11.14 283 
11.14 107 
11.13 931 

11.13 757 
11.13 583 
11.13 409 
11.13 237 
11.13 065 
11.12 894 
11.12 723 
11.12 553 
11.12 384 
11.12 215 

11.12 047 
11.11880 
11.11713 
11.11547 
11.11382 

11.11217 
11.11052 
11.10 889 
11.10 726 
11.10 563 
11.10 402 
11.10 240 
11.10 080 
11.09 920 
11.09 760 
11.09 601 
11.09 443 
11.09 285 
11.09 128 
11.08 971 

11.08 815 
11.08 660 
11.08 505 
11.08 350 
11.08 197 
11.08 043 
11.07 890 
11.07 738 
11.07 586 
11.07 435 

11.07 284 
11.07 134 
11.06 984 
11.06 835 
11.06 687 
11.06 538 
11.06 391 
11.06 244 
11.06 097 
11.05 951 

11.05 805 



L Cos 



9.99 894 
9.99 893 
9.99 892 
9.99 891 
9.99 891 

9.99 890 
9.99 889 
9.99 888 
9.99 887 
9.99 886 

9.99 885 
9.99 884 
9.99 883 
9.99 882 
9.99 881 

9.99 880 
9.99 879 
9.99 879 
9.99 878 
9.99 877 
9.99 876 
9.99 875 
9.99 874 
9.99 873 
9.99 872 

9.99 871 
9.99 870 
9.99 869 
9.99 868 
9.99 867 

9.99 866 
9.99 865 
9.99 864 
9.99 863 
9.99 862 

9.99 861 
9.99 860 
9.99 859 
9.99 858 
9.99 857 

9.99 856 
9.99 855 
9.99 854 
9.99 853 
9.99 852 

9.99 851 
9.99 850 
9.99 848 
9.99 847 
9.99 846 

9.99 845 
9.99 844 
9.99 843 
9.99 842 
9.99 841 
9.99 840 
9.99 839 
9.99 838 
9.99 837 
9.99 836 

9.99 834 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 



181 

36.2 

54.3 

72.4 

90.5 

108.6 

126.7 

144.8 

162.9 

177 
35.4 
53.1 
70.8 

88.5 
106.2 
123.9 
141.6 
159.3 

171 

34.2 

51.3 

68.4 
85.5 
102.6 
119.7 
136.8 
153.9 

167 

33.4 

50.1 

66.8 

83.5 

100.2 

116.9 

133.6 

150.3 

161 

32.2 

48.3 

64.4 

80.5 

96.6 

112.7 

128.8 

144.9 



157 

31.4 

47.1 

62.8 

78.5 

94.2 

109.9 

125.6 

141.3 

151 



180 

36.0 

54.0 

72.0 

90.0 

108.0 

126.0 

144.0 

162.0 



175 

35.0 
52.5 

70.0 
87.5 
105.0 
122.5 
140.0 
157.5 

170 

34.0 

51.0 

68.0 

85.0 

102.0 

119.0 

136.0 

153.0 



165 

33.0 

49.5 

66.0 

82.5 

99.0 

115.5 

132.0 

148.5 



160 

32.0 

48.0 

64.0 

80.0 

96.0 

112.0 

128.0 

144.0 

155 

31.0 

46.5 
62.0 
77.5 
93.0 

108.5 
124.0 
139.5 

150 



2 


30.2 


30.0 


3 


45.3 


45.0 


4 


60.4 


60.0 


5 


75.5 


75.0 


6 


90.6 


90.0 


7 


105.7 


105.0 


8 


120.8 


120.0 


9 


135.9 


135.0 




147 


145 


2 


29.4 


29.0 


3 


44.1 


43.5 


4 


58.8 


58.0 


5 


73.5 


72.5 


6 


88.2 


87.0 


7 


102.9 


101.5 


8 


117.6 


116.0 


9 


132.3 


130.5 



179 

35.8 

53.7 

71.6 

89.5 

107.4 

125.3 

143.2 

161.1 

173 

34.6 

51.9 

69.2 

86.5 

103.8 

121.1 

138.4 

155.7 

169 

33.8 

50.7 

67.6 

84.5 

101.4 

118.3 

135.2 

152.1 

163 

32.6 

48.9 

65.2 

81.5 

97.8 

114.1 

130.4 

146.7 



159 

31.8 

47.7 

63.6 

79.5 

95.4 

111.3 

127.2 

143.1 

153 

30.6 

45.9 

61.2 

76.5 

91.8 

107.1 

122.4 

137.7 

149 

29.8 

44.7 

59.6 

74.5 

89.4 

104.3 

119.2 

134.1 

144 

28.8 

43.2 

57.6 

72.0 

86.4 

100.8 

115.2 

129.6 



Prop. Pts. 



85° — Logarithms of Trigonometric Functions 



Ill] 



5° — Logarithms of Trigonometric Functions 



51 



LSin 



LTan 



cd 



LCtn 



L Cos 



Prop. Pts. 





1 
2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 

24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 

42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



8.94 030 
8.94 174 
8.94 317 
8.94 461 
8.94 603 

8.94 746 

8.94 887 

8.95 029 
8.95 170 
8.95 310 

8.95 450 
8.95 589 
8.95 728 

8.95 867 

8.96 005 

8.96 143 
8.96 280 
8.96 417 
8.96 553 
8.96 689 

8.96 825 

8.96 960 

8.97 095 
8.97 229 
8.97 363 
8.97 496 
8.97 629 
8.97 762 

8.97 894 

8.98 026 

8.98 157 
8.98 288 
8.98 419 
8.98 549 
8.98 679 



98 808 

98 937 

99 066 
99 194 
99 322 

99 450 
99 577 
99 704 
99 830 
99 956 
00 082 
00 207 
00 332 
00 456 
00 581 
00 704 
00 828 

00 951 

01 074 
01 196 
01 318 
01 440 
,01 561 
,01 682 
,01 803 
01 923 



LCos 



144 
143 
144 
142 
143 

141 
142 
141 
140 
140 

139 
139 
139 
138 
138 

137 
137 
136 
136 
136 
135 
135 
134 
134 
133 

133 
133 
132 
132 
131 

131 
131 
130 
130 
129 

129 
129 
128 
128 
128 

127 
127 
126 
126 
126 

125 
125 

124 
125 
123 
124 
123 
123 
122 
122 

122 
121 
121 
121 
120 



8.94 195 
8.94 340 
8.94 485 
8.94 630 
8.94 773 

8.94 917 

8.95 060 
8.95 202 
8.95 344 
8.95 486 

8.95 627 
8.95 767 

8.95 908 

8.96 047 
8.96 187 

8.96 325 
8.96 464 
8.96 602 
8.96 739 

8.96 877 

8.97 013 
8.97 150 
8.97 285 
8.97 421 
8.97 556 

8.97 691 
8.97 825 

8.97 959 

8.98 092 
8.98 225 

8.98 358 
8.98 490 
8.98 622 
8.98 753 

8.98 884 

8.99 015 
8.99 145 
8.99 275 
8.99 405 
8.99 534 

8.99 662 
8.99 791 
8.99 919 
9.00 046 
9.00 174 

9.00 301 
9.00 427 
9.00 553 
9.00 679 
9.00 805 

9.00 930 

9.01 055 
9.01 179 
9.01 303 
9.01 427 
9.01 550 
9.01 673 
9.01 796 

9.01 918 

9.02 040 

9.02 162 



145 
145 
145 
143 
144 

143 
142 
142 
142 
141 

140 
141 
139 
140 
138 

139 
138 
137 
138 
136 

137 
135 
136 
135 
135 
134 
134 
133 
133 
133 
132 
132 
131 
131 
131 

130 
130 
130 
129 
128 
129 
128 
127 
128 
127 
126 
126 
126 
126 
125 
125 
124 
124 
124 
123 
123 
123 
122 
122 
122 



11.05 805 
11.05 660 
11.05 515 
11.05 370 
11.05 227 

11.05 083 
11.04 940 
11.04 798 
11.04 656 
11.04 514 

11.04 373 
11.04 233 
11.04 092 
11.03 953 
11.03 813 
11.03 675 
11.03 536 
11.03 398 
11.03 261 
11.03 123 

11.02 987 
11.02.850 
11.02 715 
11.02 579 
11.02 444 

11.02 309 
11.02 175 
11.02 041 
11.01 908 
11.01 775 
11.01 642 
11.01510 
11.01 378 
11.01 247 
11.01 116 

11.00 985 
11.00 855 
11.00 725 
11.00 595 
11.00 466 
11.00 338 
11.00 209 
11.00 081 
10.99 954 
10.99 826 

10.99 699 
10.99 573 
10.99 447 
10.99 321 
10.99 195 

10.99 070 
10.98 945 
10.98 821 
10.98 697 
10.98 573 
10.98 450 
10.98 327 
10.98 204 
10.98 082 
10.97 960 
10.97 838 



d L Ctn c d L Tan L Sin 



9.99 834 
9.99 833 
9.99 832 
9.99 831 
9.99 830 

9.99 829 
9.99 828 
9.99 827 
9.99 825 
9.99 824 

9.99 823 
9.99 822 
9.99 821 
9.99 820 
9.99 819 

9.99 817 
9.99 816 
9.99 815 
9.99 814 
9.99 813 

9.99 812 
9.99 810 
9.99 809 
9.99 808 
9.99 807 

9.99 806 
9.99 804 
9.99 803 
9.99 802 
9.99 801 
9.99 800 
9.99 798 
9.99 797 
9.99 796 
9.99 795 

9.99 793 
9.99 792 
9.99 791 
9.99 790 
9.99 788 

9.99 787 
9.99 786 
9.99 785 
9.99 783 
9.99 782 

9.99 781 
9.99 780 
9.99 778 
9.99 777 
9.99 776 

9.99 775 
9.99 773 
9.99 772 
9.99 771 
9.99 769 
9.99 768 
9.99 767 
9.99 765 
9.99 764 
9.99 763 
9.99 761 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 

1 





143 

28.6 

42.9 

57.2 

71.5 

85.8 

100.1 

114.4 

128.7 

140 

28.0 
42.0 
56.0 
70.0 
84.0 
98.0 
112.0 
126.0 

137 

27.4 
41.1 
54.8 
68.5 
82.2 
95.9 
109.6 
123.3 



134 

26.8 
40.2 
53.6 
67.0 
80.4 
93.8 
107.2 
120.6 

131 

26.2 
39.3 
52.4 
65.5 
78.6 
91.7 
104.8 
117.9 

128 

25.6 
38.4 
51.2 
64.0 
76.8 
89.6 
102.4 
115.2 

125 

25.0 
37.5 
50.0 
62.5 
75.0 
87.5 
100.0 
112.5 

122 

24.4 
36.6 
48.8 
61.0 
73.2 
85.4 
97.6 
109.8 



142 

28.4 
42.6 
56.8 
71.0 
85.2 
99.4 
113.6 
127.8 

139 
27.8 
41.7 
55.6 
69.5 
83.4 
97.3 
111.2 
125.1 

136 
27.2 
40.8 
54.4 
68.0 
81.6 
95.2 
108.8 
122.4 



133 

26.6 
39.9 
53.2 
66.5 
79.8 
93.1 
106.4 
119.7 

130 

26.0 
39.0 
52.0 
65.0 
78.0 
91.0 
104.0 
117.0 

127 

25.4 

38.1 

50.8 
63.5 
76.2 
88.9 
101.6 
114.3 

124 

24.8 
37.2 
49.6 
62.0 
74.4 
86.8 
99.2 
111.6 

121 

24.2 
36.3 
48.4 
60.5 
72.6 
84.7 
96.8 
108.9 



141 

28.2 
42.3 
56.4 
70.5 
84.6 
98.7 
112.8 
126.9 

138 

27.6 
41.4 
55.2 
69.0 
82.8 
96.6 
110.4 
124.2 

135 

27.0 
40.5 
54.0 
67.5 
81.0 
94.5 
108.0 
121.5 

132 

26.4 
39.6 
52.8 
66.0 
79.2 
92.4 
105.6 
118.8 

129 
25.8 
38.7 
51.6 
64.5 
77.4 
90.3 
103.2 
116.1 



126 
25.2 
37.8 
50.4 
63.0 
75.6 
88.2 
100.8 
113.4 

123 

24.6 
36.9 
49.2 
61.5 
73.8 
86.1 
98.4 
110.7 

120 

24.0 
36.0 
48.0 
60.0 
72.0 
84.0 
96.0 
108.0 



Prop. Pts. 



84° — Logarithms of Trigonometric Functions 



52 



6° — Logarithms of Trigonometric Functions 



CHI 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 
47 
48 
49 
50 
51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.01 923 

9.02 043 
9.02 163 
9.02 283 
9.02 402 

9.02 520 
9.02 639 
9.02 757 
9.02 874 

9.02 992 

9.03 109 
9.03 226 
9.03 342 
9.03 458 
9.03 574 



03 690 
03 805 

03 920 

04 034 
04 149 
04 262 
04 376 
04 490 
04 603 
04 715 



9.04 828 

9.04 940 

9.05 052 
9.05 164 
9.05 275 

9.05 386 
9.05 497 
9.05 607 
9.05 717 
9.05 827 

9.05 937 

9.06 046 
9.06 155 
9.06 264 
9.06 372 

9.06 481 
9.06 589 
9.06 696 
9.06 804 
9.06 911 



07 018 
07 124 
07 231 
07 337 
07 442 

07 548 
07 653 
07 758 
07 863 
07 968 



9.08 072 
9.08 176 
9.08 280 
9.08 383 
9.08 486 

9.08 589 



LCos 



120 
120 
120 
119 
118 

119 
118 
117 
118 
117 

117 
116 
116 
116 
116 

115 
115 
114 
115 
113 
114 
114 
113 
112 
113 
112 
112 
112 
111 
111 

111 
110 
110 
110 
110 
109 
109 
109 
108 
109 
108 
107 
108 
107 
107 
106 
107 
106 
105 
106 

105 
105 
105 
105 
104 
104 
104 
103 
103 
103 



LTan 



9.02 162 
9.02 283 
9.02 404 
9.02 525 
9.02 645 

9.02 766 

9.02 885 

9.03 005 
9.03 124 
9.03 242 

9.03 361 
9.03 479 
9.03 597 
9.03 714 
9.03 832 

9.03 948 

9.04 065 
9.04 181 
9.04 297 
9.04 413 

9.04 528 
9.04 643 
9.04 758 
9.04 873 

9.04 987 

9.05 101 
9.05 214 
9.05 328 
9.05 441 
9.05 553 

9.05 666 
9.05 778 

9.05 890 

9.06 002 
9.06 113 

9.06 224 
9.06 335 
9.06 445 
9.06 556 
9.06 666 

9.06 775 
9.06 885 

9.06 994 

9.07 103 
9.07 211 

9.07 320 
9.07 428 
9.07 536 
9.07 643 
9.07 751 

9.07 858 

9.07 964 

9.08 071 
9.08 177 
9.08 283 

9.08 389 
9.08 495 
9.08 600 
9.08 705 
9.08 810 
9.08 914 



cd 



L Ctn c d 



121 
121 
121 
120 
121 

119 
120 
119 
118 
119 

118 
118 
117 
118 
116 

117 
116 
116 
116 
115 
115 
115 
115 
114 
114 

113 
114 
113 
112 
113 
112 
112 
112 
111 
111 

111 
110 
111 

110 
109 

110 

109 
109 
108 
109 

108 

108 
107 
108 
107 
106 
107 
106 
106 
106 
106 
105 
105 
105 
104 



LCtn 



10.97 838 
10.97 717 
10.97 596 
10.97 475 
10.97 355 

10.97 234 
10.97 115 
10.96 995 
10.96 876 
10.96 758 
10.96 639 
10.96 521 
10.96 403 
10.96 286 
10.96 168 
10.96 052 
10.95 935 
10.95 819 
10.95 703 
10.95 587 
10.95 472 
10.95 357 
10.95 242 
10.95 127 
10.95 013 
10.94 899 
10.94 786 
10.94 672 
10.94 559 
10.94 447 
10.94 334 
10.94 222 
10.94 110 
10.93 998 
10.93 887 

10.93 776 
10.93 665 
10.93 555 
10.93 444 
10.93 334 

10.93 225 
10.93 115 
10.93 006 
10.92 897 
10.92 789 

10.92 680 
10.92 572 
10.92 464 
10.92 357 
10.92 249 
10.92 142 
10.92 036 
10.91 929 
10.91 823 
10.91 717 
10.91 611 
10.91 505 
10.91 400 
10.91 295 
10.91 190 
10.91 086 



LTan 



LCos 



9.99 761 
9.99 760 
9.99 759 
9.99 757 
9.99 756 

9.99 755 
9.99 753 
9.99 752 
9.99 751 
9.99 749 

9.99 748 
9.99 747 
9.99 745 
9.99 744 
9.99 742 

9.99 741 
9.99 740 
9.99 738 
9.99 737 
9.99 736 

9.99 734 
9.99 733 
9.99 731 
9.99 730 
9.99 728 

9.99 727 
9.99 726 
9.99 724 
9.99 723 
9.99 721 
9.99 720 
9.99 718 
9.99 717 
9.99 716 
9.99 714 

9.99 713 
9.99 711 
9.99 710 
9.99 708 
9.99 707 

9.99 705 
9.99 704 
9.99 702 
9.99 701 
9.99 699 
9.99 698 
9.99 696 
9.99 695 
9.99 693 
9.99 692 

9.99 690 
9.99 689 
9.99 687 
9.99 686 
9.99 684 

9.99 683 
9.99 681 
9.99 680 
9.99 678 
9.99 677 

9.99 675 



LSin 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 





Prop. Pts. 





rn 


120 


119 


2 


24.2 


24.0 


23.8 


3 


36.3 


36.0 


35.7 


4 


48.4 


48.0 


47.6 


5 


60.5 


60.0 


59.5 


6 


72.6 


72.0 


71.4 


7 


84.7 


84.0 


83.3 


8 


96.8 


96.0 


95.2 


9 


108.9 


108.0 


107.1 




118 


117 


116 


2 


23.6 


23.4 


23.2 


3 


35.4 


35.1 


34.8 


4 


47.2 


46.8 


46.4 


5 


59.0 


58.5 


58.0 


6 


70.8 


70.2 


69.6 


7 


82.6 


81.9 


81.2 


8 


94.4 


93.6 


92.8 


9 


106.2 


105.3 


104.4 




115 


114 


113 


2 


23.0 


22.8 


22.6 


3 


34.5 


34.2 


33.9 


4 


46.0 


45.6 


45.2 


5 


57.5 


57.0 


56.5 


6 


69.0 


68.4 


67.8 


7 


80.5 


79.8 


79.1 


8 


92.0 


91.2 


90.4 


9 


103.5 


102.6 


101.7 




112 


111 


110 


2 


22.4 


22.2 


22.0 


3 


33.6 


33.3 


33.0 


4 


44.8 


44.4 


44.0 


5 


56.0 


55.5 


55.0 


6 


67.2 


66.6 


66.0 


7 


78.4 


77.7 


77.0 


8 


89.6 


88.8 


88.0 


9 


100.8 


99.9 


99.0 




109 


108 


107 


2 


21.8 


21.6 


21.4 


3 


32.7 


32.4 


32.1 


4 


43.6 


43.2 


42.8 


5 


54.5 


54.0 


53.5 


6 


65.4 


64.8 


64.2 


7 


76.3 


75.6 


74.9 


8 


87.2 


86.4 


85.6 


9 


98.1 


97.2 


96.3 




106 


105 


104 


2 


21.2 


21.0 


20.8 


3 


31.8 


31.5 


31.2 


4 


42.4 


42.0 


41.6 


5 


53.0 


52.5 


52.0 


6 


63.6 


63.0 


62.4 


7 


74.2 


73.5 


72.8 


8 


84.8 


84.0 


83.2 


9 


95.4 


94.5 


93.6 


J 


?rom the top: 




] 


?or 6°+ or 186°+ 


res 


id as 


printed; for 


96 


3+ or 


276°+, 


read 


co- 


-function. 





From the bottom: 

For 83°+ or 263°+, 

read as printed; for 
173°+ or 353°+ read 
co-function. 



Prop. Pte. 



83° — Logarithms of Trigonometric Functions 



Ill] 



7° — Logarithms of Trigonometric Functions 



53 



LSin 



L Tan c d 



LCtn 



LCos 



Prop. Pts. 





1 
2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



9.08 589 
9.08 692 
9.08 795 
9.08 897 

9.08 999 

9.09 101 
9.09 202 
9.09 304 
9.09 405 
9.09 506 

9.09 606 
9.09 707 
9.09 807 

9.09 907 

9.10 006 



10 106 
10 205 
10 304 
10 402 
10 501 

10 599 
10 697 
10 795 
10 893 

10 990 

11087 

11 184 
11281 
11377 
11474 

11570 
11666 
11761 
11857 
11952 



9. 

9. 
9. 
9. 
9. 
9. 
9. 
9. 
9. 
9. 

9. 
9. 
9. 
9. 
9. 

9. 
9. 
9. 
9. 
9. 

9.12 047 
9.12 142 
9.12 236 
9.12 331 
9.12 425 
9.12 519 
9.12 612 
9.12 706 
9.12 799 
9.12 892 

9.12 985 

9.13 078 
9.13 171 
9.13 263 
9.13 355 

9.13 447 
9.13 539 
9.13 630 
9.13 722 
9.13 813 
9.13 904 

9.13 994 

9.14 085 
9.14 175 
9.14 266 
9.14 356 



103 
103 
102 
102 
102 

101 
102 
101 
101 
100 

101 

100 

100 

99 

100 

99 
99 
98 
99 
98 

98 
98 
98 
97 
97 

97 
97 
96 
97 
96 

96 
95 
96 
95 
95 

95 
94 
95 
94 
94 

93 
94 
93 
93 
93 

93 
93 
92 
92 

92 

92 

91 
92 
91 
91 

90 
91 
90 
91 
90 



9.08 914 

9.09 019 
9.09 123 
9.09 227 
9.09 330 
9.09 434 
9.09 537 
9.09 640 
9.09 742 
9.09 845 

9.09 947 

9.10 049 
9.10 150 
9.10 252 
9.10 353 
9.10 454 
9.10 555 
9.10 656 
9.10 756 
9.10 856 

9.10 956 

9.11 056 
9.11 155 
9.11 254 
9.11 353 
9.11 452 
9.11 551 
9.11 649 
9.11 747 
9.11 845 

9.11 943 

9.12 040 
9.12 138 
9.12 235 
9.12 332 

9.12 428 
9.12 525 
9.12 621 
9.12 717 
9.12 813 

9.12 909 

9.13 004 
9.13 099 
9.13 194 
9.13 289 
9.13 384 
9.13 478 
9.13 573 
9.13 667 
9.13 761 

9.13 854 

9.13 948 

9.14 041 
9.14 134 
9.14 227 
9.14 320 
9.14 412 
9.14 504 
9.14 597 
9.14 688 

9.14 780 



05 
04 
04 
03 
04 

03 

03 
02 
03 
02 

02 
01 
02 
01 
01 

01 
01 
00 
00 
00 

00 
99 
99 
99 
99 

99 

98 
98 
98 
98 

97 
98 
97 
97 
96 

97 

96 
96 
96 
96 

95 

95 
95 
95 
95 
94 
95 
94 
94 
93 
94 
93 
93 
93 
93 
92 
92 
93 
91 
92 



10.91 086 
10.90 981 
10.90 877 
10.90 773 
10.90 670 

10.90 566 
10.90 463 
10.90 360 
10.90 258 
10.90 155 

10.90 053 
10.89 951 
10.89 850 
10.89 748 
10.89 647 

10.89 546 
10.89 445 
10.89 344 
10.89 244 
10.89 144 

10.89 044 
10.88944 
10.88 845 
10.88 746 
10.88 647 

10.88 548 
10.88 449 
10.88 351 
10.88 253 
10.88 155 
10.88 057 
10.87 960 
10.87 862 
10.87 765 
10.87 668 

10.87 572 
10.87 475 
10.87 379 
10.87 283 
10.87 187 
10.87 091 
10.86 996 
10.86 901 
10.86 806 
10.86 711 

10.86 616 
10.86 522 
10.86 427 
10.86 333 
10.86 239 

10.86 146 
10.86 052 
10.85 959 
10.85 866 
10.85 773 
10.85 680 
10.85 588 
10.85 496 
10.85 403 
10.85 312 

10.85 220 



9.99 675 
9.99 674 
9.99 672 
9.99 670 
9.99 669 

9.99 667 
9.99 666 
9.99 664 
9.99 663 
9.99 661 
9.99 659 
9.99 658 
9.99 656 
9.99 655 
9.99 653 

9.99 651 
9.99 650 
9.99 648 
9.99 647 
9.99 645 

9.99 643 
9.99 642 
9.99 640 
9.99 638 
9.99 637 

9.99 635 
9.99 633 
9.99 632 
9.99 630 
9.99 629 

9.99 627 
9.99 625 
9.99 624 
9.99 622 
9.99 620 

9.99 618 
9.99 617 
9.99 615 
9.99 613 
9.99 612 

9.99 610 
9.99 608 
9.99 607 
9.99 605 
9.99 603 

9,99 601 
9.99 600 
9.99 598 
9.99 596 
9.99 595 

9.99 593 
9.99 591 
9.99 589 
9.99 588 
9.99 586 

9.99 584 
9.99 582 
9.99 581 
9.99 579 
9.99 577 

9.99 575 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 

22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




105 

21.0 
31.5 
42.0 
52.5 
63.0 
73.5 
84.0 
94.5 



102 

20.4 
30.6 
40.8 
51.0 
61.2 
71.4 
81.6 
91.8 



98 

19.6 
29.4 
39.2 
49.0 

58.8 
68.6 
78.4 
88.2 



95 

19.0 

28.5 
38.0 
47.5 
57.0 
66.5 
76.0 
85.5 



92 

18.4 
27.6 
36.8 
46.0 
55.2 
64.4 
73.6 
82.8 



104 

20.8 
31.2 
41.6 
52.0 

62.4 
72.8 
83.2 
93.6 



101 

20.2 
30.3 
40.4 
50.5 
60.6 
70.7 
80.8 
90.9 



97 

19.4 
29.1 
38.8 
48.5 
58.2 
67.9 
77.6 
87.3 



94 

18.8 
28.2 
37.6 
47.0 
56.4 
65.8 
75.2 
84.6 



91 

18.2 
27.3 
36.4 
45.5 
54.6 
63.7 
72.8 
81.9 



103 
20.6 
30.9 
41.2 
51.5 
61.8 
72.1 
82.4 
92.7 



99 

19.8 
29.7 
39.6 
49.5 
59.4 
69.3 
79.2 
89.1 



96 
19.2 

28.8 
38.4 
48.0 
57.6 
67.2 
76.8 
86.4 



93 

18.6 
27.9 
37.2 
46.5 
55.8 
65.1 
74.4 
83.7 



90 

18.0 
27.0 
36.0 
45.0 
54.0 
63.0 
72.0 
81.0 



From the top: 

For 7°+ or 187°+ 
read as printed; for 
97° + or 277°+, read 
co-function. 

From the bottom: 
For 82°+ or 262°+ 
read as printed; for 
172° + or 352°+, read 
co-function. 



LCos 



LCtn 



cd 



LTan 



LSin 



Prop. Pts. 



82° — Logarithms of Trigonometric Functions 



54 



8° — Logarithms of Trigonometric Functions 



[III 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.14 356 
9.14 445 
9.14 535 
9.14 624 
9.14 714 

9.14 803 
9.14 891 

9.14 980 

9.15 069 
9.15 157 

9.15 245 
9.15 333 
9.15 421 
9.15 508 
9.15 596 



15 683 
15 770 
15 857 

15 944 

16 030 

16 116 
16 203 
16 289 
16 374 
16 460 

16 545 
16 631 
16 716 
16 801 
16 886 

16 970 

17 055 
17 139 
17 223 

17 307 

17 391 
17 474 
17 558 
17 641 
17 724 



9.17 807 
9.17 890 

9.17 973 

9.18 055 
9.18 137 

9.18 220 
9.18 302 
9.18 383 
9.18 465 
9.18 547 



18 628 
18 709 
18 790 
18 871 

18 952 

19 033 
19 113 
19 193 
19 273 
19 353 

.19 433 



LCos 



89 
90 
89 
90 
89 

88 
89 
89 
88 
88 

88 
88 
87 
88 
87 

87 
87 
87 
86 
86 

87 
86 
85 
86 
85 

86 
85 
85 
85 
84 

85 
84 
84 
84 
84 

83 
84 
83 
83 
83 

83 
83 
82 
82 
83 
82 
81 
82 
82 
81 

81 
81 
81 

81 
81 

80 
80 
80 
80 
80 



LTan 



9.14 780 
9.14 872 

9.14 963 

9.15 054 
9.15 145 
9.15 236 
9.15 327 
9.15 417 
9.15 508 
9.15 598 

9.15 688 
9.15 777 
9.15 867 

9.15 956 

9.16 046 
9.16 135 
9.16 224 
9.16 312 
9.16 401 
9.16 489 

9.16 577 
9.16 665 
9.16 753 
9.16 841 

9.16 928 

9.17 016 
9.17 103 
9.17 190 
9.17 277 
9.17 363 

9.17 450 
9.17 536 
9.17 622 
9.17 708 
9.17 794 

9.17 880 

9.17 965 

9.18 051 
9.18 136 
9.18 221 

9.18 306 
9.18 391 
9.18 475 
9.18 560 
9.18 644 

9.18 728 
9.18 812 
9.18 896 

9.18 979 

9.19 063 

9.19 146 
9.19 229 
9.19 312 
9.19 395 
9.19 478 

9.19 561 
9.19 643 
9.19 725 
9.19 807 
9.19 889 

9.19 971 



cd 



LCtn 



92 
91 
91 
91 
91 

91 
90 
91 
90 
90 

89 
90 

89 
90 
89 

89 

88 
89 
88 
88 

88 

88 
88 
87 
88 

87 
87 
87 
86 
87 
86 
86 
86 
86 
86 

85 
86 
85 
85 
85 

85 
84 
85 
84 
84 

84 
84 
83 
84 
83 

83 
83 
83 
83 
83 
82 
82 
82 
82 
82 



LCtn 



10.85 220 
10.85 128 
10.85 037 
10.84 946 
10.84 855 

10.84 764 
10.84 673 
10.84 583 
10.84 492 
10.84 402 
10.84 312 
10.84 223 
10.84 133 
10.84 044 
10.83 954 

10.83 865 
10.83 776 
10.83 688 
10.83 599 
10.83 511 

10.83 423 
10.83 335 
10.83 247 
10.83 159 
10.83 072 
10.82 984 
10.82 897 
10.82 810 
10.82 723 
10.82 637 

10.82 550 
10.82 464 
10.82 378 
10.82 292 
10.82 206 

10.82 120 
10.82 035 
10.81 949 
10.81 864 
10.81 779 
10.81 694 
10.81 609 
10.81 525 
10.81 440 
10.81 356 
10.81 272 
10.81 188 
10.81 104 
10.81 021 
10.80 937 

10.80 854 
10.80 771 
10.80 688 
10.80 605 
10.80 522 

10.80 439 
10.80 357 
10.80 275 
10.80 193 
10.80 111 
10.80 029 



LCos 



cd LTan LSin 



9.99 575 
9.99 574 
9.99 572 
9.99 570 
9.99 568 

9.99 566 
9.99 565 
9.99 563 
9.99 561 
9.99 559 

9.99 557 
9.99 556 
9.99 554 
9.99 552 
9.99 550 
9.99 548 
9.99 546 
9.99 545 
9.99 543 
9.99 541 
9.99 539 
9.99 537 
9.99 535 
9.99 533 
9,99 532 

9.99 530 
9.99 528 
9.99 526 
9.99 524 
9.99 522 

9.99 520 
9.99 518 
9.99 517 
9.99 515 
9.99 513 

9.99 511 
9.99 509 
9.99 507 
9.99 505 
9.99 503 
9.99 501 
9.99 499 
9.99 497 
9.99 495 
9.99 494 

9.99 492 
9.99 490 
9.99 488 
9.99 486 
9.99 484 
9.99 482 
9.99 480 
9.99 478 
9.99 476 
9.99 474 

9.99 472 
9.99 470 
9.99 468 
9.99 466 
9.99 464 
9.99 462 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 
40 
39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 




Prop. Pts. 



92 


91 


18.4 


18.2 


27.6 


27.3 


36.8 


36.4 


46.0 


45.5 


55.2 


54.6 


64.4 


63.7 


73.6 


72.8 


82.8 


81.9 



89 


88 


17.8 


17.6 


26.7 


26.4 


35.6 


35.2 


44.5 


44.0 


53.4 


52.8 


62.3 


61.6 


71.2 


70.4 


80.1 


79.2 



86 


85 


17.2 


17.0 


25.8 


25.5 


34.4 


34.0 


43.0 


42.5 


51.6 


51.0 


60.2 


59.5 


68.8 


68.0 


77.4 


76.5 



83 


82 


16.6 


16.4 


24.9 


24.6 


33.2 


32.8 


41.5 


41.0 


49.8 


49.2 


58.1 


57.4 


66.4 


65.6 


74.7 


73.8 



90 

18.0 
27.0 
36.0 
45.0 
54.0 
63.0 
72.0 
81.0 

87 

17.4 
26.1 

34.8 
43.5 
52.2 
60.9 
69.6 
78.3 

84 

16.8 
25.2 
33.6 
42.0 
50.4 
58.8 
67.2 
75.6 

81 

16.2 
24.3 
32.4 
40.5 
48.6 
56.7 
64.8 
72.9 



From the top: 

For 8 6+ or 188°+, 
read as printed; for 
98°+ or 278°+, read 
co-function. 

From the bottom: 
For 81° + or 261°+ 
read as printed; for 
171°+ or 351°+, read 
co-function. 



Prop. Pts. 



81° — Logarithms of Trigonometric Functions 



Ill] 



9° — Logarithms of Trigonometric Functions 



55 



LSin 





1 
2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



9.19 
9.19 
9.19 
9.19 
9.19 

9.19 
9.19 
9.19 
9.20 
9.20 

9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.20 
9.21 
9.21 
9.21 
9.21 

9.21 
9.21 
9.21 
9.21 
9.21 
9.21 
9.21 
9.21 
9.21 
9.22 

9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.22 
9.23 
9.23 
9.23 

9.23 
9,23 
9.23 
9.23 
9.23 

9.23 
.9.23 
9.23 
9.23 
9.23 

9.23 



433 
513 
592 
672 
751 

830 
909 
988 
067 
145 

223 
302 
380 
458 
535 

613 
691 
768 
845 
922 

999 
076 
153 

229 
306 
382 
458 
534 
610 
685 

761 
836 
912 

987 
062 

137 
211 
286 
361 
435 

509 
583 
657 

731 
805 

878 
952 
025 
098 
171 
244 
317 
390 
462 
535 

607 
679 
752 
823 
895 
967 



LCos d 



80 
79 
80 
79 
79 

79 

79 

79 
78 
78 

79 

78 
78 
77 
78 

78 
77 
77 
77 
77 
77 
77 
76 
77 
76 

76 
76 
76 
75 
76 

75 

76 
75 
75 
75 
74 
75 
75 
74 
74 

74 
74 
74 
74 
73 
74 
73 
73 
73 
73 

73 
73 

72 
73 

72 

72 
73 
71 

72 
72 



LTan 



9.19 971 

9.20 053 
9.20 134 
9.20 216 
9.20 297 

9.20 378 
9.20 459 
9.20 540 
9.20 621 
9.20 701 
9.20 782 
9.20 862 

9.20 942 

9.21 022 
9.21 102 
9.21 182 
9.21 261 
9.21 341 
9.21 420 
9.21 499 
9.21 578 
9.21 657 
9.21 736 
9.21 814 
9.21 893 

9.21 971 

9.22 049 
9.22 127 
9.22 205 
9.22 283 
9.22 361 
9.22 438 
9.22 516 
9.22 593 
9.22 670 

9.22 747 
9.22 824 
9.22 901 

9.22 977 

9.23 054 

9.23 130 
9.23 206 
9.23 283 
9.23 359 
9.23 435 
9.23 510 
9.23 586 
9.23 661 
9.23 737 
9.23 812 

9.23 887 

9.23 962 

9.24 037 
9.24 112 
9.24 186 

9.24 261 
9.24 335 
9.24 410 
9.24 484 
9.24 558 

9.24 632 



LCtn cd 



cd 



82 
81 
82 
81 
81 

81 
81 

81 
80 
81 

80 
80 
80 
80 
80 

79 
80 
79 
79 
79 

79 

79 
78 
79 

78 

78 
78 
78 
78 
78 

77 
78 
77 
77 
77 
77 
77 
76 
77 
76 

76 

77 
76 
76 
75 

76 
75 
76 
75 
75 
75 
75 
75 
74 
75 
74 
75 
74 
74 
74 



LCtn 



0.80 029 
0.79 947 
0.79 866 
0.79 784 
0.79 703 

0.79 622 
0.79 541 
0.79 460 
0.79 379 
0.79 299 

0.79 218 
0.79 138 
0.79 058 

0.78 978 
0.78 898 

0.78 818 
0.78 739 
0.78 659 
0.78 580 
0.78 501 
0.78 422 
0.78.343 
0.78 264 
0.78 186 
0.78 107 

0.78 029 
0.77 951 
0.77 873 
0.77 795 
0.77 717 
0.77 639 
0.77 562 
0.77 484 
0.77 407 
0.77 330 

0.77 253 
0.77 176 
0.77 099 
0.77 023 
0.76 946 

0.76 870 
0.76 794 
0.76 717 
0.76 641 
0.76 565 

0.76 490 
0.76 414 
0.76 339 
0.76 263 
0.76 188 
0.76 113 
0.76 038 
0.75 963 
0.75 888 
0.75 814 

0.75 739 
0.75 665 
0.75 590 
0.75 516 
0.75 442 

10.75 368 



L Tan L Sin 



LCos 



9.99 462 
9.99 460 
9.99 458 
9.99 456 
9.99 454 

9.99 452 
9.99 450 
9.99 448 
9.99 446 
9.99 444 

9.99 442 
9.99 440 
9.99 438 
9.99 436 
9.99 434 
9.99 432 
9.99 429 
9.99 427 
9.99 425 
9.99 423 

9.99 421 
9.99 419 
9.99 417 
9.99 415 
9.99 413 

9.99 411 
9.99 409 
9.99 407 
9.99 404 
9.99 402 

9.99 400 
9.99 398 
9.99 396 
9.99 394 
9.99 392 

9.99 390 
9.99 388 
9.99 385 
9.99 383 
9.99 381 

9.99 379 
9.99 377 
9.99 375 
9.99 372 
9.99 370 

9.99 368 
9.99 306 
9.99 364 
9.99 362 
9.99 359 

9.99 357 
9.99 355 
9.99 353 
9.99 351 
9.99 348 

9.99 346 
9.99 344 
9.99 342 
9.99 340 
9.99 337 

9.99 335 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 





Prop. Pts. 



82 


81 


16.4 


16.2 


24.6 


24.3 


32.8 


32.4 


41.0 


40.5 


49.2 


48.6 


57.4 


56.7 


65.6 


64.8 


73.8 


72.9 



79 


78 


15.8 


15.6 


23.7 


23.4 


31.6 


31.2 


39.5 


39.0 


47.4 


46.8 


55.3 


54.6 


63.2 


62.4 


71.1 


70.2 



76 


75 


15.2 


15.0 


22.8 


22.5 


30.4 


30.0 


38.0 


37.5 


45.6 


45.0 


53.2 


52.5 


60.8 


60.0 


68.4 


67.5 



73 


72 


14.6 


14.4 


21.9 


21.6 


29.2 


28.8 


36.5 


36.0 


43.8 


43.2 


51.1 


50.4 


58.4 


57.6 


65.7 


64.8 



80 

16.0 
24.0 
32.0 
40.0 
48.0 
56.0 
64.0 
72.0 

77 

15.4 
23.1 
30.8 
38.5 
46.2 
53.9 
61.6 
69.3 

74 

14.8 
22.2 
29.6 
37.0 
44.4 
51.8 
59.2 
66.6 



14.2 
21.3 
28.4 
35.5 
42.6 
49.7 
56.8 
63.9 



From the top: 

For 9°+ or 189°+, 

read as printed; for 
99°+ or 279°+ read 
co-function, 

From the bottom: 

For 80 o+ or 260°+ 

read as printed; for 
170 o+ or 350 o+ , read 
co-function. 



Prop. Pts. 



80° — Logarithms of Trigonometric Functions 



56 



10° — Logarithms of Trigonometric Functions [III 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 

14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.23 967 

9.24 039 
9,24 110 
9.24 181 
9.24 253 

9.24 324 
9.24 395 
9.24 466 
9.24 536 
9.24 607 

9.24 677 
9.24 748 
9.24 818 
9.24 888 

9.24 958 

9.25 028 
9.25 098 
9.25 168 
9.25 237 
9.25 307 

9.25 376 
9.25 445 
9.25 514 
9.25 583 
9.25 652 

9.25 721 
9.25 790 
9.25 858 
9.25 927 

9.25 995 

9.26 063 
9.26 131 
9.26 199 
9.26 267 
9.26 335 

9.26 403 
9.26 470 
9.26 538 
9.26 605 
9.26 672 



26 739 
26 806 
26 873 

26 940 

27 007 
27 073 
27 140 
27 206 
27 273 
27 339 

27 405 
27 471 
27 537 
27 602 

27 668 

9.27 734 
9.27 799 
9.27 864 
9.27 930 

9.27 995 

9.28 060 



LCos 



72 
71 
71 
72 
71 

71 
71 
70 

71 
70 

71 
70 
70 
70 
70 

70 

70 
69 
70 
69 

69 
69 
69 
69 
69 

69 

68 
69 
68 
68 

68 
68 
68 
68 
68 

67 

68 
67 
67 
67 

67 
67 
67 
67 
66 

67 
66 
67 
66 
66 

66 
66 
65 
66 
66 

65 
65 
66 
65 
65 



LTan 



24 632 
24 706 
24 779 
24 853 

24 926 

25 000 
25 073 
25 146 
25 219 

25 292 

25 365 
25 437 
25 510 
25 582 
25 655 

25 727 
25 799 
25 871 

25 943 

26 015 

26 086 
26 158 
26 229 
26 301 
26 372 

26 443 
26 514 
26 585 
26 655 

26 726 

26 797 
26 867 

26 937 

27 008 
27 078 
27148 
27 218 
27 288 
27 357 
27 427 
27 496 
27 566 
27 635 
27 704 
27 773 
27 842 
27 911 

27 980 

28 049 
28 117 

28 186 
28 254 
28 323 
28 391 
28 459 

28 527 
28 595 
28 662 
28 730 
28 798 

28 865 



LCtn cd 



cd 



74 
73 
74 
73 

74 

73 
73 
73 
73 
73 

72 
73 
72 
73 
72 
72 
72 
72 
72 
71 
72 
71 
72 
71 
71 
71 
71 
70 
71 
71 

70 
70 
71 
70 
70 

70 

70 
69 
70 
69 

70 

69 
69 
69 
69 

69 
69 
69 
68 
69 

68 
69 
68 
68 
68 

68 
67 
68 
68 
67 



LCtn 



10.75 368 
10.75 294 
10.75 221 
10.75 147 
10.75 074 

10.75 000 
10.74 927 
10.74 854 
10.74 781 
10.74708 

10.74 635 
10.74 563 
10.74490 
10.74418 
10.74345 

10.74 273 
10.74 201 
10.74 129 
10.74 057 
10.73 985 
10.73 914 
10.73 842 
10.73 771 
10.73 699 
10.73 628 

10.73 557 
10.73 486 
10.73 415 
10.73 345 
10.73 274 
10.73 203 
10.73 133 
10.73 063 
10.72 992 
10.72 922 

10.72 852 
10.72 782 
10.72 712 
10.72 643 
10.72 573 

10.72 504 
10.72 434 
10.72 365 
10.72 296 
10.72 227 
10.72 158 
10.72 089 
10.72 020 
10.71 951 
10.71 883 
10.71 814 
10.71746 
10.71 677 
10.71 609 
10.71 541 

10.71 473 
10.71405 
10.71 338 
10.71 270 
10.71 202 

10.71 135 



LCos d 



9.99 335 
9.99 333 
9.99 331 
9.99 328 
9.99 326 

9.99 324 
9.99 322 
9.99 319 
9.99 317 
9.99 315 

9.99 313 
9.99 310 
9.99 308 
9.99 306 
9.99 304 

9.99 301 
9.99 299 
9.99 297 
9.99 294 
9.99 292 

9.99 290 
9.99 288 
9.99 285 
9.99 283 
9.99 281 
9.99 278 
9.99 276 
9.99 274 
9.99 271 
9.99 269 

9.99 267 
9.99 264 
9.99 262 
9.99 260 
9.99 257 
9.99 255 
9.99 252 
9.99 250 
9.99 248 
9.99 245 

9.99 243 
9.99 241 
9.99 238 
9.99 236 
9.99 233 
9.99 231 
9.99 229 
9.99 226 
9.99 224 
9.99 221 
9.99 219 
9.99 217 
9.99 214 
9.99 212 
9.99 209 

9.99 207 
9.99 204 
9.99 202 
9.99 200 
9.99 197 
9.99 195 



LTan I LSin d ' 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 




Prop. Pts. 



74 


73 


14.8 


14.6 


22.2 


21.9 


29.6 


29.2 


37.0 


36.5 


44.4 


43.8 


51.8 


51.1 


59.2 


58.4 


66.6 


65.7 



71 


70 


14.2 


14.0 


21.3 


21.0 


28.4 


28.0 


35.5 


35.0 


42.6 


42.0 


49.7 


49.0 


56.8 


56.0 


63.9 


63.0 



68 


67 


13.6 


13.4 


20.4 


20.1 


27.2 


26.8 


34.0 


33.5 


40.8 


40.2 


47.6 


46.9 


54.4 


53.6 


61.2 


60.3 



65 


3 


13.0 


0.6 


19.5 


0.9 


26.0 


1.2 


32.5 


1.5 


39.0 


1.8 


45.5 


2.1 


52.0 


2.4 


58.5 


2.7 



72 

14.4 
21.6 
28.8 
36.0 
43.2 
50.4 
57.6 
64.8 

69 

13.8 
20.7 
27.6 
34.5 
41.4 
48.3 
55.2 
62.1 

66 

13.2 
19.8 
26.4 
33.0 
39.6 
46.2 
52.8 
59.4 

2 

0.4 
0.6 
0.8 
1.0 
1.3 
1.4 
1.6 
1.8 



From the top: 

Forl0 o+ orl90 o+ , 
read as printed ; for 
100 o+ or280 o+ ,read 

co-function. 

From the bottom: 
For79 0+ or259 0+ , 
read as printed ; for 
169° + or349° + ,read 
co-function. 



Prop. Pts. 






79° — Logarithms of Trigonometric Functions 



Ill] 11° — Logarithms of Trigonometric Functions 



57 



7 
8 
9 
10 
11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 

53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.28 060 
9.28 125 
9.28 190 
9.28 254 
9.28 319 

9.28 384 
9.28 448 
9.28 512 

9.28 577 
9.28 641 

9.28 705 
9.28 769 
9.28 833 
9.28 896 

9.28 960 

9.29 024 
9.29 087 
9.29 150 
9.29 214 
9.29 277 
9.29 340 
9.29 403 
9.29 466 
9.29 529 
9.29 591 

9.29 654 
9.29 716 
9.29 779 
9.29 841 
9.29 903 

9.29 966 

9.30 028 
9.30 090 
9.30 151 
9.30 213 

9.30 275 
9.30 336 
9.30 398 
9.30 459 
9.30 521 
9.30 582 
9.30 643 
9.30 704 
9.30 765 
9.30 826 
9.30 887 

9.30 947 

9.31 008 
9.31 068 
9.31 129 



.31 189 
.31 250 
.31310 
.31 370 
.31 430 

.31 490 
.31 549 
.31 609 
.31 669 
.31 728 



9.31 788 



65 
65 
64 
65 
65 
64 
64 
65 
64 
64 

64 
64 
63 
64 
64 

63 
63 
64 
63 
63 

63 
63 
63 
62 
63 
62 
63 
62 
62 
63 

62 
62 
61 
62 
62 

61 
62 
61 
62 
61 

61 
61 
61 
61 
61 

60 
61 
60 
61 
60 
61 
60 
60 
60 
60 

59 
60 
60 
59 
60 



LTan 



9.28 865 

9.28 933 

9.29 000 
9.29 067 
9.29 134 

9.29 201 
9.29 268 
9.29 335 
9.29 402 
9.29 468 

9.29 535 
9.29 601 
9.29 668 
9.29 734 
9.29 800 

9.29 866 
9.29 932 

9.29 998 

9.30 064 
9.30 130 

9.30 195 
9.30 261 
9.30 326 
9.30 391 
9.30 457 
9.30 522 
9.30 587 
9.30 652 
9.30 717 
9.30 782 

9.30 846 
9.30 911 

9.30 975 

9.31 040 
9.31 104 

9.31 168 
9.31 233 
9.31 297 
9.31 361 
9.31 425 
9.31 489 
9.31 552 
9.31 616 
9.31 679 
9.31 743 
9.31 806 
9.31 870 
9.31 933 

9.31 996 

9.32 059 

9.32 122 
9.32 185 
9.32 248 
9.32 311 
9.32 373 

9.32 436 
9.32 498 
9.32 561 
9.32 623 
9.32 685 
9.32 747 



cd 



68 
67 
67 
67 
67 

67 

67 
67 
66 
67 
66 
67 
66 
66 
66 
66 
66 
66 
66 
65 

66 
65 
65 
66 
65 

65 
65 
65 
65 
64 

65 
64 
65 
64 
64 

65 
64 
64 
64 
64 

63 
64 
63 
64 
63 
64 
63 
63 
63 
63 
63 
63 
63 
62 
'63 
62 
63 
62 
62 
62 



L Ctn L Cos 



LCos d LCtn cd LTan LSin d ' 



10.71 135 
10.71067 
10.71 000 
10.70 933 
10.70866 

10.70 799 
10.70732 
10.70 665 
10.70598 
10.70 532 

10.70 465 
10.70 399 
10.70 332 
10.70 266 
10.70 200 
10.70 134 
10.70 068 
10.70 002 
10.69 936 
10.69 870 

10.69805 
10.69 739 
10.69 674 
10.69 609 
10.69 543 
10.69 478 
10.69 413 
10.69 348 
10.69 283 
10.69 218 

10.69 154 
10.69 089 
10.69 025 
10.68 960 
10.68 896 

10.68 832 
10.68 767 
10.68 703 
10.68 639 
10.68 575 

10.68 511 
10.68448 
10.68 384 
10.68 321 
10.68 257 
10.68 194 
10.68130 
10.68 067 
10.68 004 
10.67 941 
10.67 878 
10.67 815 
10.67 752 
10.67 689 
10.67 627 

10.67564 
10.67502 
10.67439 
10.67 377 
10.67 315 
10.67 253 



9.99 195 
9.99 192 
9.99 190 
9.99 187 
9.99 185 
9.99 182 
9.99 180 
9.99 177 
9.99 175 
9.99 172 

9.99 170 
9.99 167 
9.99 165 
9.99 162 
9.99 160 
9.99 157 
9.99 155 
9.99 152 
9.99 150 
9.99 147 

9.99 145 
9.99 142 
9.99 140 
9.99 137 
9.99 135 
9.99 132 
9.99 130 
9.99 127 
9.99 124 
9.99 122 

9.99 119 
9.99 117 
9.99114 
9.99112 
9.99 109 
9.99 106 
9.99 104 
9.99 101 
9.99 099 
9.99 096 

9.99 093 
9.99 091 
9.99 088 
9.99 086 
9.99 083 
9.99 080 
9.99 078 
9.99 075 
9.99 072 
9.99 070 

9.99 067 
9.99 064 
9.99 062 
9.99 059 
9.99 056 
9.99 054 
9.99 051 
9.99 048 
9.99 046 
9.99 043 

9.99 040 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 

42 
41 

40 

39 
38 
37 
36 
35 
34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 





Prop. Pts. 



68 


67 


13.6 


13.4 


20.4 


20.1 


27.2 


26.8 


34.0 


33.5 


40.8 


40.2 


47.6 


46.9 


54.4 


53.6 


61.2 


60.3 



65 


64 


13.0 


12.8 


19.5 


19.2 


26.0 


25.6 


32.5 


32.0 


39.0 


38.4 


45.5 


44.8 


52.0 


51.2 


58.5 


57.6 



62 


61 


12.4 


12.2 


18.6 


18.3 


24.8 


24.4 


31.0 


30.5 


37.2 


36.6 


43.4 


42.7 


49.6 


48.8 


55.8 


54.9 



59 


3 


11.8 


0.6 


17.7 


0.9 


23.6 


1.2 


29.5 


1.5 


35.4 


1.8 


41.3 


2.1 


47.2 


2.4 


53.1 


2.7 



66 

13.2 

19.8 
26.4 
33.0 
39.6 
46.2 
52.8 
59.4 

63 

12.6 
18.9 
25.2 
31.5 
37.8 
44.1 
50.4 
56.7 

60 

12.0 
18.0 
24.0 
30.0 
36.0 
42.0 
48.0 
54.0 

2 

0.4 
0.6 
0.8 
1.0 
1.2 
1.4 
1.6 
1.8 



From the top: 

ForH 0+ orl91 0+ , 

read as printed; for 
101 o+ or281 o+ ,read 
co-function. 

From the bottom: 
For73 0+ or258 0+ , 
read as printed ; for 
168 0+ or348 0+ ,read 
co-function. 



Prop. Pts. 



78° — Logarithms of Trigonometric Functions 



58 



12° — Logarithms of Trigonometric Functions 



CHI 



o 

i 

2 
3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.31 788 
9.31 847 
9.31 907 

9.31 966 

9.32 025 

9.32 084 
9.32 143 
9.32 202 
9.32 261 
9.32 319 

9.32 378 
9.32 437 
9.32 495 
9.32 553 
9.32 612 

9.32 670 
9.32 728 
9.32 786 
9.32 844 
9.32 902 

9.32 960 

9.33 018 
9.33 075 
9.33 133 
9.33 190 



.33 248 
.33 305 
.33 362 
.33 420 

.33 477 

.33 534 
.33 591 
.33 647 
.33 704 
.33 761 



9.33 818 
9.33 874 
9.33 931 

9.33 987 

9.34 043 
9.34 100 
9.34 156 
9.34 212 
9.34 268 
9.34 324 

9.34 380 
9.34 436 
9.34 491 
9.34 547 
9.34 602 



.34 658 
.34 713 
.34 769 
.34 824 
.34 879 
.34 934 
.34 989 
.35 044 
.35 099 
.35 154 



9.35 209 



LCos 



59 
60 
59 
59 
59 

59 
59 
59 
58 
59 

59 

58 
58 
59 
58 

58 

58 
58 
58 
58 

58 
57 
58 
57 
58 

57 
57 
58 
57 
57 

57 
56 
57 
57 
57 

56 
57 
56 
56 
57 

56 
56 
56 
56 
56 

56 
55 
56 
55 
56 

55 

56 
55 
55 
55 

55 
55 
55 
55 
55 



LTan 



9.32 747 
9.32 810 
9.32 872 
9.32 933 

9.32 995 

9.33 057 
9.33 119 
9.33 180 
9.33 242 
9.33 303 
9.33 365 
9.33 426 
9.33 487 
9.33 548 
9.33 609 
9.33 670 
9.33 731 
9.33 792 
9.33 853 
9.33 913 

9.33 974 

9.34 034 
9.34 095 
9.34 155 
9.34 215 

9.34 276 
9.34 336 
9.34 396 
9.34 456 
9.34 516 

9.34 576 
9.34 635 
9.34 695 
9.34 755 
9.34 814 

9.34 874 
9.34 933 

9.34 992 

9.35 051 
9.35 111 

9.35 170 
9.35 229 
9.35 288 
9.35 347 
9.35 405 
9.35 464 
9.35 523 
9.35 581 
9.35 640 
9.35 698 

9.35 757 
9.35 815 
9.35 873 
9.35 931 

9.35 989 

9.36 047 
9.36 105 
9.36 163 
9.36 221 
9.36 279 

9.36 336 



cd LCtn 



63 
62 
61 
62 
62 
62 
61 
62 
61 
62 

61 
61 
61 
61 
61 

61 

61 
61 
60 
61 

60 
61 
60 
60 
61 

60 
60 
60 
60 
60 

59 
60 
60 
59 
60 

59 
59 
59 
60 
59 

59 
59 
59 

58 
59 

59 

58 
59 
58 
59 

58 
58 
58 
58 
58 

58 
58 
58 
58 
57 



10.67 253 
10.67 190 
10.67 128 
10.67 067 
10.67 005 

10.66 943 
10.66 881 
10.66 820 
10.66 758 
10.66 697 
10.66 635 
10.66 574 
10.66 513 
10.66 452 
10.66 391 

10.66 330 
10.66 269 
10.66 208 
10.66 147 
10.66 087 

10.66 026 
10.65 966 
10.65 905 
10.65 845 
10.65 785 

10.65 724 
10.65 664 
10.65 604 
10.65 544 
10.65 484 

10.65 424 
10.65 365 
10.65 305 
10.65 245 
10.65 186 
10.65 126 
10.65 067 
10.65 008 
10.64 949 
10.64 889 

10.64 830 
10.64 771 
10.64 712 
10.64 653 
10.64 595 

10.64 536 
10.64 477 
10.64 419 
10.64 360 
10.64 302 

10.64 243 
10.64 185 
10.64 127 
10.64 069 
10.64 011 
10.63 953 
10.63 895 
10.63 837 
10.63 779 
10.63 721 
10.63 664 



L Cos 



LCtn cd LTan LSin d 



9.99 040 
9.99 038 
9.99 035 
9.99 032 
9.99 030 
9.99 027 
9.99 024 
9.99 022 
9.99 019 
9.99 016 
9.99 013 
9.99 011 
9.99 008 
9.99 005 
9.99 002 

9.99 000 
9.98 997 
9.98 994 
9.98 991 
9.98 989 

9.98 986 
9.98 983 
9.98 980 
9.98 978 
9.98 975 

9.98 972 
9.98 969 
9.98 967 
9.98 964 
9.98 961 

9.98 958 
9.98 955 
9.98 953 
9.98 950 
9.98 947 
9.98 944 
9.98 941 
9.98 938 
9.98 936 
9.98 933 

9.98 930 
9.98 927 
9.98 924 
9.98 921 
9.98919 

9.98 916 
9.98 913 
9.98 910 
9.98 907 
9.98 904 

9.98 901 
9.98 898 
9.98 896 
9.98 893 
9.98 890 

9.98 887 
9.98 884 
9.98 881 
9.98 878 
9.98 875 

9.98 872 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 
50 
49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 



63 


62 


12.6 


12.4 


18.9 


18.6 


25.2 


24.8 


31.5 


31.0 


37.8 


37.2 


44.1 


43.4 


50.4 


49.6 


56.7 


55.8 





60 


59 


2 


12.0 


11.8 


3 


18.0 


17.7 


4 


24.0 


23.6 


5 


30.0 


29.5 


6 


36.0 


35.4 


7 


42.0 


41.3 


8 


48.0 


47.2 


9 


54.0 


53.1 



61 

12.2 
18.3 
24.4 
30.5 
36.6 
42.7 
48.8 
54.9 

58 

11.6 
17.4 
23.2 
29.0 
34.8 
40.6 
46.4 
52.2 





57 


2 


11.4 


3 


17.1 


4 


22.8 


5 


28.5 


6 


34.2 


7 


39.9 


8 


45.6 


9 


51.3 



56 

11.2 
16.8 
22.4 
28.0 
33.6 
39.2 
44.8 
50.4 



55 


3 


11,0 


0.6 


16.5 


0.9 


22.0 


1.2 


27.5 


1.5 


33.0 


1.8 


38.5 


2.1 


44.0 


2.4 


49.5 


2.7 



2 

0.4 
0.6 
0.8 
1.0 
1.2 
1.4 
1.6 
1.8 



From the top: 

Forl2 0+ orl92 0+ , 

read as printed ; for 
102 o+ or282 o+ ,read 
co-function. 

From the bottom: 
For77 0+ or257 0+ , 
read as printed ; for 
167°+ or 347°+ read 
co-function. 



Prop. Pts. 



77° — Logarithms of Trigonometric Functions 



Ill] 13° — Logarithms of Trigonometric Functions 



59 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin 



35 209 
35 263 
35 318 
35 373 
35 427 

35 481 
35 536 
35 590 
35 644 
35 698 
35 752 
35 806 
35 860 
35 914 

35 968 

36 022 
36 075 
36 129 
36 182 
36 236 
36 289 
36 342 
36 395 
36 449 
36 502 

36 555 

36 608 
36 660 
36 713 
36 766 
36 819 
36 871 
36 924 

36 976 

37 028 

37 081 
37 133 
37 185 

37 237 
37 289 
37 341 
37 393 
37 445 
37 497 
37 549 

37 600 
37 652 
37 703 
37 755 

37 806 

37 858 
37 909 

37 960 

38 011 
38 062 

38 113 
38 164 
38 215 
38 2G6 
38 317 

38 368 



54 
55 
55 
54 
54 

55 

54 
54 
54 
54 
54 
54 
54 
54 
54 

53 
54 
53 
54 
53 

53 
53 
54 
53 
53 

53 
52 
53 
53 
53 
52 
53 
52 
52 
53 

52 
52 
52 
52 
52 

52 
52 
52 
52 
51 

52 
51 
52 
51 
52 

51 
51 
51 
51 
51 
51 
51 
51 
51 
51 



LTan cd 



9.36 336 
9.36 394 
9.36 452 
9.36 509 
9.36 566 

9.36 624 
9.36 681 
9.36 738 
9.36 795 
9.36 852 

9.36 909 

9.36 966 

9.37 023 
9.37 080 
9.37 137 
9.37 193 
9.37 250 
9.37 306 
9.37 363 
9.37 419 
9.37 476 
9.37 532 
9.37 588 
9.37 644 
9.37 700 

9.37 756 
9.37 812 
9.37 868 
9.37 924 

9.37 980 

9.38 035 
9.38 091 
9.38 147 
9.38 202 
9.38 257 

9.38 313 
9.38 368 
9.38423 
9.38 479 
9.38 534 

9.38 589 
9.38 644 
9.38 699 
9.38 754 
9.38 808 

9.38 863 
9.38 918 

9.38 972 

9.39 027 
9.39 082 

9.39 136 
9.39 190 
9.39 245 
9.39 299 
9.39 353 
9.39 407 
9.39 461 
9.39 515 
9.39 569 
9.39 623 

9.39 677 



58 
58 
57 
57 

58 

57 
57 
57 
57 
57 
57 
57 
57 
57 
56 

57 
56 
57 
56 
57 
56 
56 
56 
56 
56 
56 
56 
56 
56 
55 

56 
56 
55 
55 
56 
55 
55 
56 
55 
55 

55 

55 
55 
54 
55 

55 

54 
55 
55 
54 

54 
55 
54 
54 
54 

54 
54 
54 
54 
54 



L Ctn L Cos 



0.63 664 
0.63 606 
0.63 548 
0.63 491 
0.63 434 

0.63 376 
0.63 319 
0.63 262 
0.63 205 
0.63 148 

0.63 091 
0.63 034 
0.62 977 
0.62 920 
0.62 863 
0.62 807 
0.62 750 
0.62 694 
0.62 637 
0.62 581 
0.62 524 
0.62 468 
0.62 412 
0.62 356 
0.62 300 
0.62 244 
0.62 188 
0.62 132 
0.62 076 
0.62 020 
0.61 965 
0.61909 
0.61 853 
0.61798 
0.61 743 

0.61 687 
0.61632 
0.61577 
0.61521 
0.61 466 
0.61411 
0.61356 
0.61301 
0.61 246 
0.61 192 

0.61 137 
0.61 082 
0.61 028 
0.60 973 
0.60 918 

0.60 864 
0.60 810 
0.60755 
0.60 701 
0.60 647 
0.60 593 
0.60539 
0.60485 
0.60431 
0.60 377 
0.60323 



9.98 872 
9.98 869 
9.98 867 
9.98 864 
9.98 861 
9.98 858 
9.98 855 
9.98 852 
9.98 849 
9.98 846 

9.98 843 
9.98 840 
9.98 837 
9.98 834 
9.98 831 
9.98 828 
9.98 825 
9.98 822 
9.98 819 
9.98 816 
9.98 813 
9.98 810 
9.98 807 
9.98 804 
9.98 801 

9.98 798 
9.98795 
9.98 792 
9.98 789 
9.98 786 
9.98 783 
9.98 780 
9.98777 
9.98 774 
9.98 771 

9.98768 
9.98765 
9.98 762 
9.98 759 
9.98 756 
9.98 753 
9.98 750 
9.98 746 
9.98743 
9.98 740 

9.98 737 
9.98 734 
9.98 731 
9.98 728 
9.98725 
9.98 722 
9.98719 
9.98715 
9.98 712 
9.98 709 

9.98 706 
9.98 703 
9.98700 
9.98697 
9.98 694 

9.98 690 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 
50 
49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 



58 


57 


11.6 


11.4 


17.4 


17.1 


23.2 


22.8 


29.0 


28.5 


34.8 


34.2 


40.6 


39.9 


46.4 


45.6 


52.2 


51.3 



55 


54 


11.0 


10.8 


16.5 


16.2 


22.0 


21.6 


27.5 


27.0 


33.0 


32.4 


38.5 


37.8 


44.0 


43.2 


49.5 


48.6 



56 

11.2 

16.8 
22.4 
28.0 
33.6 
39.2 
44.8 
50.4 

53 

10.6 
15.9 
21.2 
26.5 
31.8 
37.1 
42.4 
47.7 





52 


2 


10.4 


3 


15.6 


4 


20.8 


5 


26.0 


6 


31.2 


7 


36.4 


8 


41.6 


9 


46.8 



51 

10.2 
15.3 
20.4 
25.5 
30.6 
35.7 
40.8 
45.9 



4 


3 


0.8 


0.6 


1.2 


0.9 


1.6 


1.2 


2.0 


1.5 


2.4 


1.8 


2.8 


2.1 


3.2 


2.4 


3.6 


2.7 



2 

0.4 
0.6 
0.8 
1.0 
1.2 
1.4 
1.6 
1.8 



From the top: 

Forl3 0+ orl93 0+ , 
read as printed; for 
103 o+ or283 o+ ,read 
co-function. 

From the bottom: 

For 76°+ or 256°+ 
read as printed; for 
166°+ or 346°+ read 
co-function. 



LCos d 



LCtn cd 



LTan LSin d 



Prop. Pts. 



76° — Logarithms of Trigonometric Functions 



60 



14° — Logarithms of Trigonometric Functions [III 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 

12 
13 

14 

15 

16 
17 

18 
19 

20 

21 
22 
23 

24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 

47 
48 
49 

50 

51 
52 
53 

54 

55 

56 
57 
58 
59 
60 



LSin 



9.38 368 
9.38 418 
9.38 469 
9.38 519 
9.38 570 
9.38 620 
9.38 670 
9.38 721 
9.38 771 
9.38 821 

9.38 871 
9.38 921 

9.38 971 

9.39 021 
9.39 071 

9.39 121 
9.39 170 
9.39 220 
9.39 270 
9.39 319 
9.39 369 
9.39 418 
9.39 467 
9.39 517 
9.39 566 

9.39 615 
9.39 664 
9.39 713 
9.39 762 
9.39 811 



39 860 
39 909 

39 958 

40 006 
40 055 

40 103 
.40 152 
40 200 
40 249 
40 297 

40 346 
40 394 
40 442 
.40 490 
40 538 

40 586 
.40 634 
.40 682 
.40 730 
.40 778 
.40 825 
.40 873 
.40 921 
.40 968 
.41 016 
.41 063 
.41 111 
.41 158 
.41 205 
.41 252 

.41 300 



LCos 



50 
51 
50 
51 
50 

50 
51 
50 
50 
50 

50 
50 
50 
50 
50 

49 
50 
50 
49 
50 
49 
49 
50 
49 
49 
49 
49 
49 
49 
49 

49 

49 
48 
49 

48 

49 

48 
49 
48 
49 

48 
48 
48 
48 
48 

48 

48 
48 
48 
47 

48 
48 
47 
48 
47 
48 
47 
47 
47 
48 



LTan 



9.39 677 
9.39 731 
9.39 785 
9.39 838 
9.39 892 

9.39 945 

9.39 999 

9.40 052 
9.40 106 
9.40 159 
9.40 212 
9.40 266 
9.40 319 
9.40 372 
9.40 425 

9.40 478 
9.40 531 
9.40 584 
9.40 636 
9.40 689 
9.40 742 
9.40 795 
9.40 847 
9.40 900 

9.40 952 

9.41 005 
9.41 057 
9.41 109 
9.41 161 
9.41 214 

9.41 266 
9.41 318 
9.41 370 
9.41 422 
9.41 474 
9.41 526 
9.41 578 
9.41 629 
9.41 681 
9.41 733 

9.41 784 
9.41 836 
9.41 887 
9.41 939 

9.41 990 

9.42 041 
9.42 093 
9.42 144 
9.42 195 
9.42 246 

9.42 297 
9.42 348 
9.42 399 
9.42 450 
9.42 501 
9.42 552 
9.42 603 
9.42 653 
9.42 704 
9.42 755 
9.42 805 



LCtn 



cd 



54 
54 
53 
54 
53 
54 
53 
54 
53 
53 

54 
53 
53 
53 
53 
53 
53 
52 
53 
53 

53 
52 
53 
52 
53 
52 
52 
52 
53 
52 

52 

52 
52 
52 
52 

52 
51 
52 
52 
51 
52 
51 
52 
51 
51 
52 
51 
51 
51 
51 

51 

51 
51 
51 
51 

51 

50 
51 
51 
50 



LCtn 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10. 

10. 
10. 
10. 
10. 

10. 
10. 
10. 
10, 
10, 
10. 
10, 
10, 
10, 
10, 
10 



60 323 
60269 
60215 
60162 
60108 

60 055 
60 001 
59 948 
59 894 
59 841 

59 788 
59 734 
59 681 
59 628 
59 575 
59 522 
59 469 
59416 
59 364 
59 311 
59 258 
59 205 
59153 
59100 
59 048 

58 995 
58 943 
58 891 
58 839 

58786 

58734 
58 682 
58 630 
58 578 
58526 
58474 
58422 
58371 
58 319 
58 267 

58 216 
58 164 
58113 
58 061 
58 010 

57959 
57 907 
57 856 
,57 805 
57 754 

,57 703 
,57 652 
,57 601 
,57550 
,57499 

,57448 
,57397 
.57 347 
.57 296 
.57 245 

.57 195 



cd LTan LSin d 



LCos 



9.98 690 
9.98 687 
9.98 684 
9.98 681 
9.98 678 
9.98 675 
9.98 671 
9.98 668 
9.98 665 
9.98 662 

9.98 659 
9.98 656 
9.98 652 
9.98 649 
9.98 646 

9.98 643 
9.98 640 
9.98 636 
9.98 633 
9.98 630 

9.98 627 
9.98 623 
9.98 620 
9.98 617 
9.98 614 

9.98 610 
9.98 607 
9.98 604 
9.98 601 
9.98597 
9.98 594 
9.98 591 
9.98 588 
9.98 584 
9.98581 

9.98 578 
9.98 574 
9.98 571 
9.98 568 
9.98565 

9.98 561 
9.98 558 
9.98 555 
9.98 551 
9.98 548 

9.98 545 
9.98 541 
9.98 538 
9.98 535 
9.98 531 

9.98 528 
9.98 525 
9.98 521 
9.98 518 
9.98 515 

9.98 511 
9.98 508 
9.98 505 
9.98 501 
9.98 498 
9.98 494 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 
30 
29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 



54 


53 


10.8 


10.6 


16.2 


15.9 


21.6 


21.2 


27.0 


26.5 


32.4 


31.8 


37.8 


37.1 


43.2 


42.4 


48.6 


47.7 



51 


50 


10.2 


10.0 


15.3 


15.0 


20.4 


20.0 


25.5 


25.0 


30.6 


30.0 


35.7 


35.0 


40.8 


40.0 


45.9 


45.0 



52 

10.4 
15.6 
20.8 
26.0 
31.2 
36.4 
41.6 
46.8 

49 

9.8 
14.7 
19.6 
24.5 
29.4 
34.3 
39.2 
44.1 





48 


2 


9.6 


3 


14.4 


4 


19.2 


5 


24.0 


6 


28.8 


7 


33.6 


8 


38.4 


9 


43.2 



47 

9.4 
14.1 
18.8 
23.5 
28.2 
32.9 
37.6 
42.3 

3 

0.6 
0.9 
1.2 
1.5 
1.8 
2.1 
2.4 
2.7 



From the top: 
Forl4° + orl94° + , 
read as printed; for 
104 o+ or284 o+ ,read 
co-function. 

From the bottom: 
For75 0+ or255 0+ , 
read as printed; for 
165° + or345° + ,read 
co-function. 





4 


2 


0.8 


3 


1.2 


4 


1.6 


5 


2.0 


6 


2.4 


7 


2.8 


8 


3.2 


9 


3.6 



Prop. Pte. 






75° — Logarithms of Trigonometric Functions 



Ill] 15° — Logarithms of Trigonometric Functions 



61 



LSin 



LTan cd 



L Ctn L Cos d 



Prop. Pts. 





1 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 

42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



9.41 
9.41 
9.41 
9.41 
9.41 

9.41 
9.41 
9.41 
9.41 
9.41 

9.41 
9.41 
9.41 
9.41 
9.41 

9.42 
9.42 
9.42 
9.42 
9.42 

9.42 
9.42 
9.42 
9.42 
9.42 

9.42 
9.42 
9.42 
9.42 
9.42 

9.42 
9.42 
9.42 
9.42 
9.42 

9.42 
9.42 
9.43 
9.43 
9.43 

9.43 
9.43 
9.43 
9.43 
9.43 

9.43 
9.43 
9.43 
9.43 
9.43 

9.43 
9.43 
9.43 
9.43 
9.43 
9.43 
9.43 
9.43 
9.43 
9.43 
9.44 



300 
347 
394 
441 

488 

535 

582 
628 
675 

722 

768 
815 
861 
908 
954 

001 
047 
093 
140 
186 
232 
278 
324 
370 
416 
461 
507 
553 
599 
644 

690 
735 

781 
826 

872 

917 
962 
008 
053 
098 
143 
188 
233 
278 
323 

367 
412 
457 
502 
546 

591 
635 
680 
724 
769 
813 
857 
901 
946 
990 
034 



47 
47 
47 
47 
47 

47 
46 
47 
47 
46 

47 
46 
47 
46 
47 
46 
46 
47 
46 
46 

46 
46 
46 
46 
45 
46 
46 
46 
45 
46 
45 
46 
45 
46 
45 

45 
46 
45 
45 
45 

45 
45 
45 
45 
44 

45 
45 
45 

44 
45 
44 
45 
44 
45 
44 

44 
44 
45 
44 
44 



9.42 805 
9.42 856 
9.42 906 

9.42 957 

9.43 007 

9.43 057 
9.43 108 
9.43 158 
9.43 208 
9.43 258 

9.43 308 
9.43 358 
9.43 408 
9.43 458 
9.43 508 

9.43 558 
9.43 607 
9.43 657 
9.43 707 
9.43 756 

9.43 806 
9.43 855 
9.43 905 

9.43 954 

9.44 004 

9.44 053 
9.44 102 
9.44 151 
9.44 201 
9.44 250 

9.44 299 
9.44 348 
9.44 397 
9.44 446 
9.44 495 
9.44 544 
9.44 592 
9.44 641 
9.44 690 
9.44 738 
9.44 787 
9.44 836 
9.44 884 
9.44 933 

9.44 981 

9.45 029 
9.45 078 
9.45 126 
9.45 174 
9.45 222 

9.45 271 
9.45 319 
9.45 367 
9.45 415 
9.45 463 

9.45 511 
9.45 559 
9.45 606 
9.45 654 
9.45 702 
9.45 750 



51 
50 
51 
50 
50 

51 
50 
50 
50 
50 

50 
50 
50 
50 
50 

49 
50 
50 
49 
50 
49 
50 
49 
50 
49 

49 
49 
50 
49 
49 

49 
49 
49 
49 
49 

48 
49 
49 
48 
49 

49 

48 
49 
48 
48 

49 

48 
48 
48 
49 

48 

48 
48 
48 
48 

48 
47 
48 
48 
48 



10.57 195 
10.57 144 
10.57 094 
10.57 043 
10.56 993 

10.56 943 
10.56 892 
10.56 842 
10.56 792 
10.56 742 

10.56 692 
10.56 642 
10.56 592 
10.56 542 
10.56 492 

10.56442 
10.56 393 
10.56 343 
10.56 293 
10.56 244 

10.56 i94 
10.56 145 
10.56 095 
10.56 046 
10.55 996 

10.55 947 
10.55 898 
10.55 849 
10.55 799 
10.55 750 

10.55 701 
10.55 652 
10.55 603 
10.55 554 
10.55 505 
10.55456 
10.55 408 
10.55 359 
10.55 310 
10.55 262 

10.55 213 
10.55 164 
10.55116 
10.55 067 
10.55 019 

10.54 971 
10.54 922 
10.54 874 
10.54 826 
10.54 778 
10.54 729 
10.54 681 
10.54 633 
10.54 585 
10.54 537 
10.54 489 
10.54 441 
10.54 394 
10.54 346 
10.54 298 
10.54 250 



9.98 494 
9.98491 
9.98 488 
9.98 484 
9.98 481 

9.98477 
9.98474 
9.98471 
9.98 467 
9.98464 

9.98460 
9.98457 
9.98453 
9.98 450 
9.98447 

9.98443 
9.98440 
9.98436 
9.98433 
9.98429 

9.98426 
9.98 422 
9.98419 
9.98415 
9.98 412 

9.98409 
9.98405 
9.98402 
9.98 398 
9.98 395 

9.98 391 
9.98 388 
9.98 384 
9.98 381 
9.98 377 

9.98373 
9.98 370 
9.98 366 
9.98 363 
9.98 359 

9.98 356 
9.98 352 
9.98 349 
9.98 345 
9.98 342 

9.98338 
9.98 334 
9.98 331 
9.98 327 
9.98 324 

9.98320 
9.98 317 
9.98313 
9.98 309 
9.98 306 
9.98 302 
9.98 299 
9.98 295 
9.98 291 
9.98 288 
9.98 284 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 



51 


50 


10.2 


10.0 


15.3 


15.0 


20.4 


20.0 


25.5 


25.0 


30.6 


30.0 


35.7 


35.0 


40.8 


40.0 


45.9 


45.0 



48 


47 


9.6 


9.4 


14.4 


14.1 


19.2 


18.8 


24.0 


23.5 


28.8 


28.2 


33.6 


32.9 


38.4 


37.6 


43.2 


42.3 



49 

9.8 
14.7 
19.6 
24.5 
29.4 
34.3 
39.2 
44.1 

46 
9.2 
13.8 
18.4 
23.0 
27.6 
32.2 
36.8 
41.4 





45 


2 


9.0 


3 


13.5 


4 


18.0 


5 


22.5 


6 


27.0 


7 


31.5 


8 


36.0 


9 


40.5 



2 


4 
0.8 


3 


1.2 


4 


1.6 


5 


2.0 


6 


2.4 


7 


2.8 


8 


3.2 


9 


3.6 



44 

8.8 
13.2 
17.6 
22.0 
26.4 
30.8 
35.2 
39.6 



0.6 
0.9 
1.2 
1.5 
1.8 
2.1 
2.4 
2.7 



From the top: 

Forl5 0+ orl95 0+ , 
read as printed ; for 
105 o+ or285 o+ ,read 
co-function. 

From the bottom: 

For 74°+ or 254°+ 
read as printed ; for 
164°+^>r 344°+ read 
co-function. 



LCos 



LCtn cd 



L Tan L Sin d 



Prop. Pts. 



74° — Logarithms of Trigonometric Functions 



62 



16° — Logarithms of Trigonometric Functions 



[HI 



10 

ii 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 
50 
51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin 



9.44 034 
9.44 078 
9.44 122 
9.44 166 
9.44 210 
9.44 253 
9.44 297 
9.44 341 
9.44 385 
9.44 428 



.44 472 
.44 516 
.44 559 
.44 602 
.44 646 
.44 689 
.44 733 
.44 776 
.44 819 
.44 862 



9 
9 
9 
9 
9 

9 

9 

9 

9 

9 

9.44 905 

9.44 948 

9.44 992 

9.45 035 
9.45 077 

9.45 120 
9.45 163 
9.45 206 
9.45 249 
9.45 292 
9.45 334 
9.45 377 
9.45 419 
9.45 462 
9.45 504 

9.45 547 
9.45 589 
9.45 632 
9.45 674 
9.45 716 



.45 758 
.45 801 
.45 843 
.45 885 
.45 927 

.45 969 
.46 011 
.46 053 
.46 095 
.46 136 



9.46 178 
9.46 220 
9.46 262 
9.46 303 
9.46 345 
9.46 386 
9.46 428 
9.46 469 
9.46 511 
9.46 552 

9.46 594 



L Cos 



44 
44 
44 
44 
43 
44 
44 
44 
43 
44 
44 
43 
43 
44 
43 
44 
43 
43 
43 
43 

43 

44 
43 
42 
43 

43 
43 
43 
43 
42 

43 

42 
43 
42 
43 

42 
43 

42 
42 
42 

43 

42 
42 
42 
42 

42 
42 
42 
41 
42 

42 
42 
41 
42 
41 

42 
41 
42 
41 
42 



LTan 



45 750 
45 797 
45 845 
45 892 
45 940 

45 987 

46 035 
46 082 
46 130 
46 177 
46 224 
46 271 
46 319 
46 366 
46 413 

46 460 
46 507 
46 554 
46 601 
46 648 

46 694 
46 741 

46 788 
46 835 
46 881 

46 928 

46 975 

47 021 
47 068 
47 114 

47 160 
47 207 
47 253 
47 299 
47 346 
47 392 
47 438 
47 484 
47 530 
47 576 
47 622 
47 668 
47 714 
47 760 
47 806 
47 852 
47 897 
47 943 

47 989 

48 035 
48 080 
48 126 
48 171 
48 217 
48 262 

48 307 
48 353 
48 398 
48 443 
48 489 
48 534 



LCtn cd 



cd 



47 
48 

47 
48 
47 

48 
47 
48 
47 
47 

47 

48 
47 
47 
47 
47 
47 
47 
47 
46 

47 
47 
47 
46 

47 

47 
46 
47 
46 
46 

47 
46 
46 
47 
46 

46 
46 
46 
46 
46 

46 
46 
46 
46 
46 

45 

46 
46 
46 
45 

46 
45 
46 
45 
45 

46 
45 
45 
46 

45 



L Ctn 



0.54 250 
0.54 203 
0.54 155 
0.54 108 
0.54 060 

0.54 013 
0.53 965 
0.53 918 
0.53 870 
0.53 823 
0.53 776 
0.53 729 
0.53 681 
0.53 634 
0.53 587 
0.53 540 
0.53 493 
0.53 446 
0.53 399 
0.53 352 

0.53 306 
0.53 259 
0.53 212 
0.53 165 
0.53 119 

0.53 072 
0.53 025 
0.52 979 
0.52 932 
0.52 886 

0.52 840 
0.52 793 
0.52 747 
0.52 701 
0.52 654 

0.52 608 
0.52 562 
0.52 516 
0.52 470 
0.52 424 

0.52 378 
0.52 332 
0.52 286 
0.52 240 
0.52 194 
0.52 148 
0.52 103 
0.52 057 
0.52 011 
0.51965 
0.51920 
0.51 874 
0.51829 
0.51 783 
0.51738 

0.51 693 
0.51 647 
0.51 602 
0.51557 
0.51511 

0.51466 



LCos d 



9.98 284 
9.98 281 
9.98 277 
9.98 273 
9.98 270 

9.98 266 
9.98 262 
9.98 259 
9.98 255 
9.98 251 

9.98 248 
9.98 244 
9.98 240 
9.98 237 
9.98 233 
9.98 229 
9.98 226 
9.98 222 
9.98 218 
9.98 215 
9.98 211 
9.98 207 
9.98 204 
9.98 200 
9.98 196 

9.98 192 
9.98189 
9.98 185 
9.98181 
9.98177 
9.98 174 
9.98170 
9.98166 
9.98162 
9.98159 

9.98 155 
9.98 151 
9.98 147 
9.98 144 
9.98 140 

9.98136 
9.98132 
9.98129 
9.98125 
9.98121 

9.98117 
9.98113 
9.98110 
9.98106 
9.98102 

9.98 098 
9.98 094 
9.98 090 
9.98 087 
9.98 083 
9.98 079 
9.98 075 
9.98 071 
9.98 067 
9.98 063 

9.98 060 



LTan ! LSin d 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 
30 
29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 



48 


47 


9.6 


9.4 


14.4 


14.1 


19.2 


18.8 


24.0 


23.5 


28.8 


28.2 


33.6 


32.9 


38.4 


37.6 


43.2 


42.3 



45 


44 


9.0 


8.8 


13.5 


13.2 


18.0 


17.6 


22.5 


22.0 


27.0 


26.4 


31.5 


30.8 


36.0 


35.2 


40.5 


39.6 



46 

9.2 
13.8 
18.4 
23.0 
27.6 
32.2 
36.8 
41.4 

43 

8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 





42 


2 


8.4 


3 


12.6 


4 


16.8 


5 


21.0 


6 


25.2 


7 


29.4 


8 


33.6 


9 


37.8 



41 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 

3 

0.6 
0.9 
1.2 
1.5 
1.8 
2.1 
2.4 
2.7 



From the top: 

Forl6° + orl96° + , 

read as printed ; for 
106 o+ or286 o+ ,read 
co-function. 

From the bottom: 

For73° + or253° + , 
read as printed ; for 
163° + or343° + ,read 
co-function. 





4 


2 


0.8 


3 


1.2 


4 


1.6 


5 


2.0 


6 


2.4 


7 


2.8 


8 


3.2 


9 


3.6 



Prop. Pts. 



73° — Logarithms of Trigonometric Functions 



Ill] 17° — Logarithms of Trigonometric Functions 



63 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



46 594 
46 635 
46 676 
46 717 
46 758 

46 800 
46 841 
46 882 
46 923 

46 964 

47 005 
47 045 
47 086 
47 127 
47 168 

47 209 
47 249 
47 290 
47 330 
47 371 
47 411 
47 452 
47 492 
47 533 
47 573 

47 613 

47 654 
47 694 
47 734 

47 774 

47 814 
47 854 
47 894 
47 934 

47 974 

48 014 
48 054 
48 094 
48 133 
48 173 

48 213 
48 252 
48 292 
48 332 
48 371 
48 411 
48 450 
48 490 
48 529 
48 568 
48 607 
48 647 
48 686 
48 725 
48 764 

48 803 
48 842 
48 881 
48 920 
48 959 
48 998 



LCos d 



41 
41 
41 
41 
42 
41 
41 
41 
41 
41 

40 
41 
41 
41 
41 

40 
41 
40 
41 
40 
41 
40 
41 
40 
40 
41 
40 
40 
40 
40 

40 
40 
40 
40 
40 

40 
40 
39 
40 
40 

39 
40 
40 
39 
40 

39 
40 
39 
39 
39 

40 
39 
39 
39 
39 

39 
39 
39 
39 
39 



L Tan c d 



9.48 534 
9.48 579 
9.48 624 
9.48 669 
9.48 714 

9.48 759 
9.48 804 
9.48 849 
9.48 894 
9.48 939 

9.48 984 

9.49 029 
9.49 073 
9.49 118 
9.49 163 

9.49 207 
9.49 252 
9.49 296 
9.49 341 
9.49 385 

9.49 430 
9.49 474 
9.49 519 
9.49 563 
9.49 607 

9.49 652 
9.49 696 
9,49 740 
9.49 784 
9.49 828 

9.49 872 
9.49 916 

9.49 960 

9.50 004 
9.50 048 

9.50 092 
9.50 136 
9.50 180 
9.50 223 
9.50 267 
9.50 311 
9.50 355 
9.50 398 
9.50 442 
9.50 485 

9.50 529 
9.50 572 
9.50 616 
9.50 659 
9.50 703 

9.50 746 
9.50 789 
9.50 833 
9.50 876 
9.50 919 

9.50 962 

9.51 005 
9.51 048 
9.51 092 
9.51 135 
9.51 178 



LCtn cd 



45 
45 
45 
45 
45 

45 
45 
45 
45 
45 

45 

44 
45 
45 
44 

45 
44 
45 
44 
45 
44 
45 
44 
44 
45 

44 
44 
44 
44 
44 

44 
44 
44 
44 
44 

44 
44 
43 
44 
44 
44 
43 
44 
43 
44 

43 
44 
43 
44 
43 

43 
44 
43 
43 
43 

43 
43 
44 
43 
43 



LCtn 



10.51466 
10.51421 
10.51376 
10.51331 
10.51 286 
10.51 241 
10.51 196 
10.51 151 
10.51 106 
10.51061 

10.51016 
10.50 971 
10.50 927 
10.50 882 
10.50 837 
10.50 793 
10.50 748 
10.50 704 
10.50 659 
10.50 615 
10.50 570 
10.50 526 
10.50481 
10.50437 
10.50 393 

10.50348 
10.50 304 
10.50 260 
10.50 216 
10.50 172 

10.50 128 
10.50 084 
10.50 040 
10.49 996 
10.49 952 

10.49 908 
10.49 864 
10.49 820 
10.49 777 
10.49 733 

10.49 689 
10.49 645 
10.49 602 
10.49 558 
10.49 515 
10.49 471 
10.49 428 
10.49 384 
10.49 341 
10.49 297 

10.49 254 
10.49 211 
10.49 167 
10.49 124 
10.49 081 
10.49 038 
10.48 995 
10.48 952 
10.48 908 
10.48 865 
10.48 822 



LTan 



LCos d 



9.98 060 
9.98 056 
9.98 052 
9.98 048 
9.98 044 
9.98 040 
9.98 036 
9.98 032 
9.98 029 
9.98 025 
9.98 021 
9.98 017 
9.98 013 
9.98 009 
9.98 005 

9.98 001 
9.97 997 
9.97 993 
9.97 989 
9.97 986 

9.97 982 
9.97 978 
9.97 974 
9.97 970 
9.97 966 

9.97 962 
9.97 958 
9.97 954 
9.97 950 
9.97 946 
9.97 942 
9.97 938 
9.97 934 
9.97 930 
9.97 926 
9.97 922 
9.97 918 
9.97 914 
9.97 910 
9.97 906 
9.97 902 
9.97 898 
9.97 894 
9.97 890 
9.97 886 
9.97 882 
9.97 878 
9.97 874 
9.97 870 
9.97 866 

9.97 861 
9.97 857 
9.97 853 
9.97 849 
9.97 845 
9.97 841 
9.97 837 
9.97 833 
9.97 829 
9.97 825 

9.97 821 



LSin d 



d 






60 


4 


59 


4 


58 


4 


57 


4 
4 


56 


55 


4 


54 


4 


53 


3 


52 


4 


51 


4 


50 


4 


49 


4 


48 


4 


47 


4 


46 


4 


45 


4 


44 


4 


43 


4 


42 


3 


41 


4 


40 


4 


39 


4 


38 


4 


37 


4 
4 


36 


35 


4 


34 


4 


33 


4 


32 


4 


31 


4 


30 


4 


29 


4 


28 


4 


27 


4 


26 


4 


25 


4 


24 


4 


23 


4 


22 


4 


21 


4 


20 


4 


19 


4 


18 


4 


17 


4 


16 


4 


15 


4 


14 


4 


13 


4 


12 


4 
5 


11 


10 


4 


9 


4 


8 


4 


7 


4 


6 


4 


5 


4 


4 


4 


3 


4 


2 


4 


1 


4 





d 


t 



Prop. Pts. 



45 


44 


9.0 


8.8 


13.5 


13.2 


18.0 


17.6 


22.5 


22.0 


27.0 


26.4 


31.5 


30.8 


36.0 


35.2 


40.5 


39.6 



42 


41 


8.4 


8.2 


12.6 


12.3 


16.8 


16.4 


21.0 


20.5 


25.2 


24.6 


29.4 


28.7 


33.6 


32.8 


37.8 


36.9 



43 

8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 

40 

8.0 
12.0 
16.0 
20.0 
24.0 
28.0 
32.0 
36.0 





39 


2 


7.8 


3 


11.7 


4 


15.6 


5 


19.5 


6 


23.4 


7 


27.3 


8 


31.2 


9 


35.1 



5 

1.0 
1.5 
2.0 
2.5 
3,0 
3.5 
4.0 
4.5 

3 

0.6 
0.9 
1.2 
1.5 

1.8 
2.1 
2.4 

2.7 



From the top: 
For 17°+ or 197°+ 
read as printed ; for 
107°+ or 287°+, read 
co-function. 

From the bottom: 

For72° + or252°+ 
read as printed; for 
162 0+ or342 0+ ,read 
co-function. 





4 


2 


0.8 


3 


1.2 


4 


1.6 


5 


2.0 


6 


2.4 


7 


2.8 


8 


3.2 


9 


3.6 



Prop. Pts. 



72° — Logarithms of Trigonometric Functions 



64 



18° — Logarithms of Trigonometric Functions [III 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 

14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.48 998 

9.49 037 
9.49 076 
9.49 115 
9.49 153 

9.49 192 
9.49 231 
9.49 269 
9.49 308 
9.49 347 

9.49 385 
9.49 424 
9.49 462 
9.49 500 
9.49 539 

9.49 577 
9.49 615 
9.49 654 
9.49 692 
9.49 730 
9.49 768 
9.49 806 
9.49 844 
9.49 882 
9.49 920 

9.49 958 

9.49 996 

9.50 034 
9.50 072 
9.50 110 

9.50 148 
9.50 185 
9.50 223 
9.50 261 
9.50 298 

9.50 336 
9.50 374 
9.50 411 
9.50 449 
9.50 486 

9.50 523 
9.50 561 
9.50 598 
9.50 635 
9.50 673 

9.50 710 
9.50 747 
9.50 784 
9.50 821 
9.50 858 



.50 896 
.50 933 
.50 970 
.51 007 
.51 043 
.51 080 
.51 117 
.51 154 
.51 191 
.51 227 
.51 264 



39 
39 
39 
38 
39 

39 
38 
39 
39 
38 

39 

38 
38 
39 
38 

38 
39 
38 
38 
38 

38 

38 
38 
38 
38 

38 
38 
38 
38 
38 

37 

38 
38 
37 
38 

38 
37 
38 
37 
37 

38 
37 
37 
38 
37 

37 
37 
37 
37 
38 

37 

37 
37 
36 
37 

37 
37 
37 
36 
37 



LTan cd L Ctn L Cos d 



9.51 178 
9.51 221 
9.51 264 
9.51 306 
9.51 349 

9.51 392 
9.51 435 
9.51 478 
9.51 520 
9.51 563 
9.51 606 
9.51 648 
9.51 691 
9.51 734 
9.51 776 

9.51 819 
9.51 861 
9.51 903 
9.51 946 

9.51 988 

9.52 031 
9.52 073 
9.52 115 
9.52 157 
9.52 200 

9.52 242 
9.52 284 
9.52 326 
9.52 368 
9.52 410 

9.52 452 
9.52 494 
9.52 536 
9.52 578 
9.52 620 
9.52 661 
9.52 703 
9.52 745 
9.52 787 
9.52 829 

9.52 870 
9.52 912 
9.52 953 

9.52 995 

9.53 037 
9.53 078 
9.53 120 
9.53 161 
9.53 202 
9.53 244 

9.53 285 
9.53 327 
9.53 368 
9.53 409 
9.53 450 

9.53 492 
9.53 533 
9.53 574 
9.53 615 
9.53 656 
9.53 697 



43 

43 
42 
43 
43 

43 
43 
42 
43 
43 

42 
43 
43 
42 
43 

42 

42 
43 
42 
43 

42 
42 
42 
43 
42 

42 
42 
42 
42 
42 

42 
42 
42 
42 
41 

42 
42 
42 
42 
41 

42 
41 
42 
42 
41 

42 
41 
41 
42 
41 

42 
41 
41 
41 

42 

41 

41 
41 
41 
41 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10, 
10. 
10, 
10, 
10 

10, 
10 
10 
10, 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 
10 



48 822 
48 779 
48 736 
48 694 
48 651 

48 608 
48 565 
48 522 
48 480 
48437 
48 394 
48 352 
48 309 
48 266 
48 224 

48181 
48139 
48 097 
48 054 
48 012 

47 969 

47 927 
47 885 
47 843 
47 800 

47 758 
47 716 
47 674 
47 632 
47 590 

47 548 
47 506 
47464 
47 422 
47 380 

47 339 
47 297 
47 255 
47 213 
47 171 
47 130 
,47 088 
,47 047 
47 005 
,46 963 

,46 922 

,46 880 
.46 839 
.46 798 
.46 756 

.46 715 
.46 673 
.46 632 
.46 591 
.46 550 

.46 508 
.46467 
.46 426 
.46 385 
.46 344 
.46 303 



9.97 821 
9.97 817 
9.97 812 
9.97 808 
9.97 804 

9.97 800 
9.97 796 
9.97 792 
9.97 788 
9.97 784 

9.97779 
9.97 775 
9.97 771 
9.97 767 
9.97 763 
9.97 759 
9.97 754 
9.97750 
9.97 746 
9.97 742 

9.97738 
9.97 734 
9.97 729 
9.97 725 
9.97 721 

9.97 717 
9.97 713 
9.97 708 
9.97 704 
9.97700 

9.97 696 
9.97 691 
9.97 687 
9.97 683 
9.97 679 
9.97 674 
9.97 670 
9.97 666 
9.97 662 
9.97 657 
9.97 653 
9.97 649 
9.97 645 
9.97 640 
9.97 636 
9.97 632 
9.97 628 
9.97 623 
9.97 619 
9.97 615 

9.97 610 
9.97 606 
9.97 602 
9.97597 
9.97 593 

9.97 589 
9.97 584 
9.97 580 
9.97 576 
9.97 571 

9.97 567 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 



43 


42 


8.6 


8.4 


12.9 


12.6 


17.2 


16.8 


21.5 


21.0 


25.8 


25.2 


30.1 


29.4 


34.4 


33.6 


38.7 


37.8 



39 


38 


7.8 


7.6 


11.7 


11.4 


15.6 


15.2 


19.5 


19.0 


23.4 


22.8 


27.3 


26.6 


31.2 


30.4 


35.1 


34.2 



36 


5 


7.2 


1.0 


10.8 


1.5 


14.4 


2.0 


18.0 


2.5 


21.6 


3.0 


25.2 


3.5 


28.8 


4.0 


32.4 


4.5 



41 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 



37 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
29.6 
33.3 



4 

0.8 
1.2 
1.6 
2.0 
2.4 
2.8 
3.2 
3.6 



From the top: 
For 18°+ or 198°+ 
read as printed; for 
108°+ or 288°+ read 
co-function. 

From the bottom: 

For71° + or251° + , 
read as printed ; for 
161 0+ or341 0+ ,read 
co-function. 



LCos 



L Ctn led I LTan 



LSin 



Prop. Pts. 



71° — Logarithms of Trigonometric Functions 



Ill] 19° — Logarithms of Trigonometric Functions 



65 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 
30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 
46 
47 

48 
49 

50 

51 

52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.51 264 
9.51 301 
9.51 338 
9.51 374 
9.51411 

9.51 447 
9.51 484 
9.51 520 
9.51 557 
9.51 593 
9.51 629 
9.51 666 
9.51 702 
9.51 738 
9.51 774 
9.51 811 
9.51 847 
9.51 883 
9.51919 
9.51 955 

9.51 991 

9.52 027 
9.52 063 
9.52 099 
9.52 135 

9.52 171 
9.52 207 
9.52 242 
9.52 278 
9.52 314 

9.52 350 
9.52 385 
9.52 421 
9.52 456 
9.52 492 

9.52 527 
9.52 563 
9.52 598 
9.52 634 
9.52 669 
9.52 705 
9.52 740 
9.52 775 
9.52 811 
9.52 846 

9.52 881 
9.52 916 
9.52 951 

9.52 986 

9.53 021 



.53 056 
.53 092 
.53 126 
.53 161 
.53 196 

.53 231 
.53 266 
.53 301 
.53 336 
.53 370 

.53 405 



37 
37 
36 
37 
36 

37 
36 
37 
36 
36 

37 

36 
36 
36 
37 

36 
36 
36 
36 
36 

36 
36 
36 
36 
36 

36 
35 
36 
36 
36 

35 
36 
35 
36 
35 

36 
35 
36 
35 
36 

35 
35 
36 
35 
35 

35 
35 
35 
35 
35 

36 
34 
35 
35 
35 

35 
35 
35 
34 
35 



LTan 



L Cos d L Ctn 



9.53 697 
9.53 738 
9.53 779 
9.53 820 
9.53 861 
9.53 902 
9.53 943 

9.53 984 

9.54 025 
9.54 065 

9.54 106 
9.54 147 
9.54 187 
9.54 228 
9.54 269 

9.54 309 
9.54 350 
9.54 390 
9.54 431 
9.54 471 
9.54 512 
9.54 552 
9.54 593 
9.54 633 
9.54 673 

9.54 714 
9.54 754 
9.54 794 
9.54 835 
9.54 875 

9.54 915 
9.54 955 

9.54 995 

9.55 035 
9.55 075 

9.55 115 
9.55 155 
9.55 195 
9.55 235 
9.55 275 

9.55 315 
9.55 355 
9.55 395 
9.55 434 
9.55 474 

9.55 514 
9.55 554 
9.55 593 
9.55 633 
9.55 673 
9.55 712 
9.55 752 
9.55 791 
9.55 831 
9.55 870 

9.55 910 
9.55 949 

9.55 989 

9.56 028 
9.56 067 
9.56 107 



cd 



41 
41 
41 
41 
41 

41 
41 
41 
40 
41 

41 
40 
41 
41 
40 

41 

40 
41 
40 
41 

40 
41 
40 
40 
41 

40 
40 
41 
40 
40 

40 
40 
40 
40 
40 

40 
40 
40 
40 
40 

40 
40 
39 
40 
40 

40 
39 
40 
40 
39 

40 
39 
40 
39 
40 

39 

40 
39 
39 
40 



LCtn 



10.46 303 
10.46 262 
10.46 221 
10.46 180 
10.46 139 

10.46 098 
10.46 057 
10.46 016 
10.45 975 
10.45 935 
10.45 894 
10.45 853 
10.45 813 
10.45 772 
10.45 731 
10.45 691 
10.45 650 
10.45 610 
10.45 569 
10.45 529 

10.45 488 
10.45 448 
10.45 407 
10.45 367 
10.45 327 

10.45 286 
10.45 246 
10.45 206 
10.45 165 
10.45 125 
10.45 085 
10.45 045 
10.45 005 
10.44 965 
10.44925 
10.44 885 
10.44 845 
10.44 805 
10.44 765 
10.44 725 

10.44 685 
10.44 645 
10.44 605 
10.44 566 
10.44 526 

10.44 486 
10.44446 
10.44407 
10.44 367 
10.44327 

10.44 288 
10.44 248 
10.44 209 
10.44 169 
10.44 130 
10.44 090 
10.44 051 
10.44 011 
10.43 972 
10.43 933 
10.43 893 



L Cos d 



9.97 567 
9.97563 
9.97 558 
9.97 554 
9.97 550 

9.97 545 
9.97 541 
9.97 536 
9.97532 
9.97 528 
9.97523 
9.97 519 
9.97 515 
9.97 510 
9.97 506 
9.97 501 
9.97 497 
9.97492 
9.97488 
9.97484 

9.97479 
9.97475 
9.97470 
9.97466 
9.97461 

9.97457 
9.97453 
9.97448 
9.97444 
9.97439 

9.97435 
9.97 430 
9.97426 
9.97421 
9.97417 
9.97412 
9.97408 
9.97403 
9.97 399 
9.97 394 
9.97 390 
9.97 385 
9.97 381 
9.97 376 
9.97 372 

9.97 367 
9.97363 
9.97358 
9.97353 
9.97349 

9.97344 
9.97 340 
9.97335 
9.97 331 
9.97 326 
9.97 322 
9.97 317 
9.97 312 
9.97 308 
9.97 303 
9.97 299 



cd LTan LSin d ' 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 
35 
34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 

2 
1 





Prop. Pts. 



41 


40 


8.2 


8.0 


12.3 


12.0 


16.4 


16.0 


20.5 


20.0 


24.6 


24.0 


28.7 


28.0 


32.8 


32.0 


36.9 


36.0 



37 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
29.6 
33.3 



36 

7.2 
10.8 
14.4 
18.0 
21.6 
25.2 
28.8 
32.4 



34 


5 


6.8 


1.0 


10.2 


1.5 


13.6 


2.0 


17.0 


2.5 


20.4 


3.0 


23.8 


3.5 


27.2 


4.0 


30.6 


4.5 



39 

7.8 
11.7 
15.6 
19.5 
23.4 
27.3 
31.2 
35.1 



35 

7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 



4 

0.8 
1.2 
1.6 
2.0 
2.4 
2.8 
3.2 
3.6 



From the top: 
Forl9° + orl99°+ 
read as printed; for 
109°+ or 289°+ read 
co-function. 

From the bottom: 

For70 o+ or250 o+ , 

read as printed ; for 
160 o+ or340 o+ ,read 
co-function. 



Prop. Pts. 



70° — Logarithms of Trigonometric Functions 



66 



20° — Logarithms of Trigonometric Functions 



[HI 



LSin 





1 
2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 

23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 



53 405 
53 440 
53 475 
53 509 
53 544 

53 578 
53 613 
53 647 
53 682 
53 716 

53 751 
53 785 
53 819 
53 854 
53 888 
53 922 
53 957 

53 991 

54 025 
54 059 

54 093 
54 127 
54 161 
54 195 
54 229 
54 263 
54 297 
54 331 
54 365 
54 399 
54 433 
54 466 
54 500 
54 534 
54 567 
54 601 
54 635 
54 668 
54 702 
54 735 

54 769 
54 802 
54 836 
54 869 
54 903 

54 936 

54 969 

55 003 
55 036 
55 069 
55 102 
55 136 
55 169 
55 202 
55 235 

55 268 
55 301 
55 334 
55 367 
55 400 
55 433 



LCos 



35 
35 
34 
35 
34 

35 
34 
35 
34 
35 

34 
34 
35 
34 
34 

35 
34 
34 
34 

34 

34 
34 
34 
34 
34 

34 
34 
34 
34 
34 

33 
34 
34 
33 
34 

34 
33 
34 
33 
34 

33 
34 
33 
34 
33 

33 
34 
33 
33 
33 

34 
33 
33 
33 
33 

33 
33 
33 
33 
33 



LTan cd 



9.56 107 
9.56 146 
9.56 185 
9.56 224 
9.56 264 

9.56 303 
9.56 342 
9.56 381 
9.56 420 
9.56 459 

9.56 498 
9.56 537 
9.56 576 
9.56 615 
9.56 654 
9.56 693 
9.56 732 
9.56 771 
9.56 810 
9.56 849 

9.56 887 
9.56 926 

9.56 965 

9.57 004 
9.57 042 
9.57 081 
9.57 120 
9.57 158 
9.57 197 
9.57 235 
9.57 274 
9.57 312 
9.57 351 
9.57 389 
9.57 428 
9.57 466 
9.57 504 
9.57 543 
9.57 581 
9.57 619 

9.57 658 
9.57 696 
9.57 734 
9.57 772 
9.57 810 

9.57 849 
9.57 887 
9.57 925 

9.57 963 

9.58 001 

9.58 039 
9.58 077 
9.58 115 
9.58 153 
9.58 191 

9.58 229 
9.58 267 
9.58 304 
9.58 342 
9.58 380 

9.58 418 



LCtn cd 



39 
39 
39 
40 
39 

39 
39 
39 
39 
39 

39 
39 
39 
39 
39 

39 
39 
39 
39 
38 

39 
39 
39 
38 
39 

39 
38 
39 
38 
39 

38 
39 
38 
39 
38 

38 
39 
38 
38 
39 

38 
38 
38 
38 
39 

38 

38 
38 
38 
38 

38 
38 
38 
38 
38 

38 
37 

38 
38 
38 



LCtn 



0.43 893 
0.43 854 
0.43 815 
0.43 776 
0.43 736 

0.43 697 
0.43 658 
0.43 619 
0.43 580 
0.43 541 

0.43 502 
0.43 463 
0.43 424 
0.43 385 
0.43 346 

0.43 307 
0.43 268 
0.43 229 
0.43 190 
0.43 151 

0.43 113 
0.43 074 
0.43 035 
0.42 996 
0.42 958 
0.42 919 
0.42 880 
0.42 842 
0.42 803 
0.42 765 

0.42 726 
0.42 688 
0.42 649 
0.42 611 
0.42572 

0.42 534 
0.42 496 
0.42457 
0.42419 
0.42 381 

0.42 342 
0.42 304 
0.42 266 
0.42 228 
0.42 190 

0.42 151 
0.42113 
0.42 075 
0.42 037 
0.41 999 
0.41 961 
0.41 923 
0.41 885 
0.41 847 
0.41 809 
0.41 771 
0.41733 
0.41 696 
0.41 658 
0.41 620 
0.41 582 



LTan 



LCos 



9.97 299 
9.97294 
9.97 289 
9.97 285 
9.97 280 

9.97 276 
9.97 271 
9.97 266 
9.97 262 
9.97257 
9.97 252 
9.97 248 
9.97 243 
9.97 238 
9.97 234 

9.97 229 
9.97 224 
9.97 220 
9.97 215 
9.97210 

9.97 206 
9.97 201 
9.97 196 
9.97 192 
9.97 187 
9.97 182 
9.97 178 
9.97 173 
9.97 168 
9.97 163 
9.97 159 
9.97 154 
9.97 149 
9.97 145 
9.97 140 
9.97 135 
9.97 130 
9.97 126 
9.97121 
9.97116 
9.97111 
9.97 107 
9.97 102 
9.97097 
9.97092 

9.97087 
9.97 083 
9.97 078 
9.97073 
9.97068 

9.97 063 
9.97 059 
9.97 054 
9.97049 
9.97 044 
9.97 039 
9.97 035 
9.97 030 
9.97 025 
9.97 020 
9.97 015 



LSin 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 

1 




Prop. Pts. 



40 


39 


8.0 


7.8 


12.0 


11.7 


16.0 


15.6 


20.0 


19.5 


24.0 


23.4 


28.0 


27.3 


32.0 


31.2 


36.0 


35.1 



37 


35 


7.4 


7.0 


11.1 


10.5 


14.8 


14.0 


18.5 


17.5 


22.2 


21.0 


25.9 


24.5 


29.6 


28.0 


33.3 


31.5 



33 


5 


6.6 


1.0 


9.9 


1.5 


13.2 


2.0 


16.5 


2.5 


19.8 


3.0 


23.1 


3.5 


26.4 


4.0 


29.7 


4.5 



38 

7.6 
11.4 
15.2 
19.0 
22.8 
26.6 
30.4 
34.2 



34 

6.8 
10.2 
13.6 
17.0 
20.4 
23.8 
27.2 
30.6 



4 

0.8 
1.2 
1.6 
2.0 
2.4 
2.8 
3.2 
3.6 



From the top: 

For 20°+ or 200°+ 

read as printed ; for 
110 o+ or290 o+ ,read 
co-function. 

From the bottom: 

For69 0+ or249 0+ , 
read as printed; for 
159° + or339°+ read 
co-function. 



Prop. Pts. 



69° — Logarithms of Trigonometric Functions 



Ill] 21° — Logarithms of Trigonometric Functions 



67 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



LSin 



9.55 433 
9.55 466 
9.55 499 
9.55 532 
9.55 564 

9.55 597 
9.55 630 
9.55 663 
9.55 695 
9.55 728 

9.55 761 
9.55 793 
9.55 826 
9.55 858 
9.55 891 

9.55 923 
9.55 956 

9.55 988 

9.56 021 
9.56 053 

9.56 085 
9.56 118 
9.56 150 
9.56 182 
9.56 215 

9.56 247 
9.56 279 
9.56 311 
9.56 343 
9.56 375 

9.56 408 
9.56 440 
9.56 472 
9.56 504 
9.56 536 

9.56 568 
9.56 599 
9.56 631 
9.56 663 
9.56 695 



.56 727 
.56 759 
56 790 
56 822 
.56 854 

56 886 
.56 917 
.56 949 

56 980 

57 012 

57 044 
57 075 
57 107 
57 138 
57 169 

57 201 
57 232 
57 264 
57 295 
57 326 

57 358 



LCos 



33 

33 
33 
32 
33 

33 
33 
32 
33 
33 

32 
33 
32 
33 
32 

33 
32 
33 
32 
32 

33 
32 
32 
33 
32 

32 
32 
32 
32 
33 

32 
32 
32 
32 
32 

31 

32 
32 
32 
32 

32 
31 
32 
32 
32 

31 

32 
31 
32 

32 

31 
32 
31 
31 

32 

31 
32 
31 
31 
32 



LTan 



9.58 418 
9.58 455 
9.58 493 
9.58 531 
9.58 569 

9.58 606 
9.58 644 
9.58 681 
9.58 719 
9.58 757 

9.58 794 
9.58 832 
9.58 869 
9.58 907 
9.58 944 

9.58 981 

9.59 019 
9.59 056 
9.59 094 
9.59 131 

9.59 168 
9.59 205 
9.59 243 
9.59 280 
9.59 317 
9.59 354 
9.59 391 
9.59 429 
9.59 406 
9.59 503 

9.59 540 
9.59 577 
9.59 614 
9.59 651 
9.59 688 

9.59 725 
9.59 762 
9.59 799 
9.59 835 
9.59 872 

9.59 909 
9.59 946 

9.59 983 

9.60 019 
9.60 056 

9.60 093 
9.60 130 
9.60 166 
9.60 203 
9.60 240 

9.60 276 
9.60 313 
9.60 349 
9.60 386 
9.60 422 

9.60 459 
9.60 495 
9.60 532 
9.60 568 
9.60 605 

9.60 641 



LCtn 



cd LCtn 



37 

38 
38 
38 
37 

38 
37 
38 
38 
37 

38 
37 
38 
37 
37 

38 
37 
38 
37 
37 

37 
38 
37 
37 
37 

37 
38 
37 
37 
37 

37 
37 
37 
37 
37 

37 
37 
36 
37 
37 

37 
37 
36 
37 
37 

37 
36 
37 
37 
36 

37 
36 
37 
36 
37 

36 
37 
36 
37 
36 



.41 582 
,41545 
.41 507 
,41469 
,41431 
41 394 
41356 
41319 
41281 
41 243 

41 206 
41 168 
41 131 
41 093 
41 056 

41 019 
40 981 
40 944 
40 906 
40869 

40 832 
40 795 
40 757 
40 720 
40 683 

40 646 
40 609 
40 571 
40534 
40497 

40460 
40423 
40386 
40 349 
40 312 

40 275 
40 238 
40 201 
40165 
40128 

40 091 
40 054 
40 017 
39 981 
39 944 

39 907 
39 870 
39 834 
39 797 
39 760 

39 724 
39 687 
39 651 
39 614 
39 578 

39 541 
39 505 
39 468 
39 432 
39 395 
39 359 



cd LTan 



LCos d 



9.97 015 
9.97010 
9.97 005 
9.97001 
9.96 996 

9.96 991 
9.96 986 
9.96 981 
9.96 976 
9.96 971 

9.96 966 
9.96 962 
9.96 957 
9.96 952 
9.96 947 

9.96 942 
9.96 937 
9.96 932 
9.96 927 
9.96 922 

9.96 917 
9.96 912 
9.96 907 
9.96 903 
9.96 898 

9.96 893 
9.96 888 
9.96 883 
9.96 878 
9.96 873 

9.96 868 
9.96 863 
9.96 858 
9.96 853 
9.96 848 

9.96 843 
9.96 838 
9.96 833 
9.96 828 
9.96 823 

9.96 818 
9.96 813 
9.96 808 
9.96 803 
9.96 798 

9.96 793 

9.96 788 
9.96 783 
9.96 778 
9.96 772 

9.96 767 
9.96 762 
9.96 757 
9.96 752 
9.96 747 

9.96 742 
9.96 737 
9.96 732 
9.96 727 
9.96 722 

9.96 717 



LSin d ' 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 
14 
13 
12 
11 

10 

9 
8 

7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 



38 


37 


7.6 


7.4 


11.4 


11.1 


15.2 


14.8 


19.0 


18.5 


22.8 


22.2 


26.6 


25.9 


30.4 


29.6 


34.2 


33.3 



33 


32 


6.6 


6.4 


9.9 


9.6 


13.2 


12.8 


16.5 


16.0 


19.8 


19.2 


23.1 


22.4 


26.4 


25.6 


29.7 


28.8 



6 


5 


1.2 


1.0 


1.8 


1.5 


2.4 


2.0 


3.0 


2.5 


3.6 


3.0 


4.2 


3.5 


4.8 


4.0 


5.4 


4.5 



36 

7.2 
10.8 
14.4 
18.0 
21.6 
25.2 
28.8 
32.4 



31 

6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 



4 

0.8 
1.2 
1.6 
2.0 
2.4 
2.8 
3.2 
3.6 



From the top: 
For21 o+ or201 o+ , 
read as printed; for 
111°+ or 291°+ read 
co-function. 

From the bottom: 
For68° + or248°+ 
read as printed; for 
158°+ or 338°+ read 
co-function. 



Prop. Pts. 



68° — Logarithms of Trigonometric Functions 



68 



22° — Logarithms of Trigonometric Functions 



CHI 



o 

i 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 

42 
43 
44 

45 
46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.57 358 
9.57 389 
9.57 420 
9.57 451 
9.57 482 

9.57 514 
9.57 545 
9.57 576 
9.57 607 
9.57 638 

9.57 669 
9.57 700 
9.57 731 
9.57 762 
9.57 793 

9.57 824 
9.57 855 
9.57 885 
9.57 916 
9.57 947 

9.57 978 

9.58 008 
9.58 039 
9.58 070 
9.58 101 

9.58 131 
9.58 162 
9.58 192 
9.58 223 
9.58 253 

9.58 284 
9.58 314 
9.58 345 
9.58 375 
9.58 406 

9.58 436 
9.58 467 
9.58 497 
9.58 527 
9.58 557 

9.58 588 
9.58 618 
9.58 648 
9.58 678 
9.58 709 

9.58 739 
9.58 769 
9.58 799 
9.58 829 
9.58 859 



.58 889 
.58 919 
.58 949 
.58 979 
.59 009 

.59 039 
.59 069 
.59 098 
.59 128 
.59 158 
.59 188 



LCos 



31 

31 
31 
31 
32 

31 
31 
31 
31 
31 

31 
31 
31 
31 
31 

31 

30 
31 
31 
31 

30 
31 
31 
31 
30 

31 

30 
31 
30 
31 

30 
31 
30 
31 
30 

31 

30 
30 
30 
31 

30 
30 
30 
31 
30 

30 
30 
30 
30 
30 

30 
30 
30 
30 
30 

30 
29 
30 
30 
30 



LTan 



9.60 641 
9.60 677 
9.60 714 
9.60 750 
9.60 786 

9.60 823 
9.60 859 
9.60 895 
9.60 931 

9.60 967 

9.61 004 
9.61 040 
9.61 076 
9.61 112 
9.61 148 

9.61 184 
9.61 220 
9.61 256 
9.61 292 
9.61 328 

9.61 364 
9.61 400 
9.61 436 
9.61472 
9.61 508 
9.61 544 
9.61 579 
9.61 615 
9.61 651 
9.61 687 

9.61 722 
9.61 758 
9.61 794 
9.61 830 
9.61 865 

9.61 901 
9.61 936 

9.61 972 

9.62 008 
9.62 043 

9.62 079 
9.62 114 
9.62 150 
9.62 185 
9.62 221 

9.62 256 
9.62 292 
9.62 327 
9.62 362 
9.62 398 

9.62 433 
9.62 468 
9.62 504 
9.62 539 
9.62 574 

9.62 609 
9.62 645 
9.62 680 
9.62 715 
9.62 750 

9.62 785 



cd LCtn LCos d 



36 
37 
36 
36 
37 

36 
36 
36 
36 
37 

36 
36 
36 
36 
36 

36 
36 
36 
36 
36 

36 
36 
36 
36 
36 

35 
36 
36 
36 
35 

36 
36 
36 
35 
36 

35 
36 
36 
35 
36 

35 

36 
35 
36 
35 

36 
35 
35 
36 
35 

35 
36 
35 
35 
35 

36 
35 
35 
35 
35 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 



39 359 
39 323 
39 286 
39 250 
39 214 

39177 
39 141 
39105 
39 069 
39 033 

38 996 
38 960 
38 924 

38 888 
38 852 

38 816 
38 780 
38 744 
38 708 
38 672 

38 636 
38 600 
38 564 
38 528 
38492 

38 456 
38421 
38 385 
38 349 
38 313 

38 278 
38 242 
38 206 
38 170 
,38 135 

,38 099 
38 064 
,38 028 
,37 992 
,37 957 
,37 921 
,37 886 
,37 850 
,37 815 
,37 779 
,37 744 
,37 708 
,37 673 
,37 638 
,37 602 

37 567 
,37 532 
,37496 
37461 
,37426 

37 391 
37 355 
,37 320 
37285 
,37250 

,37 215 



L Ctn cd LTan 



9.96 717 
9.96 711 
9.96 706 
9.96 701 
9.96 696 

9.96 691 
9.96 686 
9.96 681 
9.96 676 
9.96 670 

9.96 665 
9.96 660 
9.96 655 
9.96 650 
9.96 645 

9.96 640 
9.96 634 
9.96 629 
9.96 624 
9.96 619 

9.96 614 
9.96 608 
9.96 603 
9.96 598 
9.96 593 

9.96 588 
9.96 582 
9.96 577 
9.96 572 
9.96 567 

9.96 562 
9.96 556 
9.96 551 
9.96 546 
9.96 541 

9.96 535 
9.96 530 
9.96 525 
9.96 520 
9.96 514 

9.96 509 
9.96 504 
9.96498 
9.96493 
9.96 488 

9.96483 
9.96477 
9.96 472 
9.96 467 
9.96 461 

9.96 456 
9.96451 
9.96445 
9.96 440 
9.96 435 

9.96429 
9.96 424 
9.96 419 
9.96413 
9.96 408 

9.96 403 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 
5 
4 
3 
2 
1 




Prop. Pts. 



37 


36 


7.4 


7.2 


11.1 


10.8 


14.8 


14.4 


18.5 


18.0 


22.2 


21.6 


25.9 


25.2 


29.6 


28.8 


33.3 


32.4 



32 


31 


6.4 


6.2 


9.6 


9.3 


12.8 


12.4 


16.0 


15.5 


19.2 


18.6 


22.4 


21.7 


25.6 


24.8 


28.8 


27.9 



29 


6 


5.8 


1.2 


8.7 


1.8 


11.6 


2.4 


14.5 


3.0 


17.4 


3.6 


20.3 


4.2 


23.2 


4.8 


26.1 


5.4 



35 

7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 



30 

6.0 
9.0 
12.0 
15.0 
18.0 
21.0 
24.0 
27.0 



5 

1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 



From the top: 
For22 o+ or202°+ 

read as printed; for 
112° + or292° + ,read 
co-function. 

From the bottom: 
For67 0+ or247 0+ , 
read as printed; for 
157° + or337° + ,read 
co-function. 



Prop. Pts. 



67° — Logarithms of Trigonometric Functions 



Ill] 23° — Logarithms of Trigonometric Functions 



69 



LSin 



d LTan 



cd LCtn 



LCos 



Prop. Pts. 





1 
2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



9.59 188 
9.59 218 
9.59 247 
9.59 277 
9.59 307 

9.59 336 
9.59 366 
9.59 396 
9.59 425 
9.59 455 

9.59 484 
9.59 514 
9.59 543 
9.59 573 
9.59 602 

9.59 632 
9.59 661 
9.59 690 
9.59 720 
9.59 749 

9.59 778 
9.59 808 
9.59 837 
9.59 866 
9.59 895 

9.59 924 
9.59 954 

9.59 983 

9.60 012 
9.60 041 

9.60 070 
9.60 099 
9.60 128 
9.60 157 
9.60 186 

9.60 215 
9.60 244 
9.60 273 
9.60 302 
9.60 331 

9.60 359 
9.60 388 
9.60 417 
9.60 446 
9.60 474 

9.60 503 
9.60 532 
9.60 561 
9.60 589 
9.60 618 



.60 646 
.60 675 
.60 704 
.60 732 
.60 761 

.60 789 
.60 818 
.60 846 
.60 875 
.60 903 
.60 931 



30 

29 
30 
30 
29 

30 
30 
29 
30 
29 

30 
29 
30 
29 
30 

29 
29 
30 
29 
29 

30 
29 
29 
29 
29 

30 

29 
29 
29 
29 

29 
29 
29 
29 
29 

29 
29 
29 
29 
28 

29 
29 
29 
28 
29 

29 
29 

28 
29 

28 

29 

29 
28 
29 

28 

29 
28 
29 
28 
28 



,62 785 
.62 820 
62 855 
62 890 
62 926 

62 961 

62 996 

63 031 
63 066 
63 101 

63 135 
63 170 
63 205 
63 240 
63 275 

63 310 
63 345 
63 379 
63 414 
63 449 

63 484 
63 519 
63 553 
63 588 
63 623 

63 657 
63 692 
63 726 
63 761 
63 796 

63 830 
63 865 
63 899 
63 934 

63 968 

64 003 
64 037 
64 072 
64 106 
64 140 

64 175 
64 209 
64 243 
64 278 
64 312 

64 346 
64 381 
64 415 
64 449 
64 483 

64 517 
64 552 
64 586 
64 620 
64 654 

64 688 
64 722 
64 756 
64 790 
64 824 

64 858 



35 
35 
35 
36 
35 

35 
35 
35 
35 
34 

35 
35 
35 
35 
35 

35 
34 
35 
35 
35 

35 
34 
35 
35 
34 

35 
34 
35 
35 
34 

35 
34 
35 
34 
35 

34 
35 
34 
34 
35 

34 
34 
35 
34 
34 

35 
34 
34 
34 
34 

35 

34 
34 
34 
34 

34 
34 
34 
34 
34 



10, 
10 
10, 
10, 
10, 

10, 
10, 
10, 
10, 
10, 

10. 
10. 
10, 
10, 
10, 

10, 
10. 
10. 
10. 
10. 

10. 
10, 
10, 
10, 
10. 

10. 
10, 
10, 
10, 
10, 

10, 
10, 
10, 
10, 
10, 

10, 
10, 
10, 
10, 
10, 

10, 
10, 
10, 
10, 
10, 

10. 
10, 
10, 
10, 
10, 

10. 
10, 
10, 
10, 
10, 

10. 
10, 
10, 
10, 
10, 
10, 



37 215 
37180 
37145 
37110 
37074 

37039 
37 004 
36 969 
36 934 
36 899 

36 865 
36 830 
36 795 
36 760 
36 725 

36 690 
36 655 
36 621 
36 586 
36 551 

36 516 

36 481 
36 447 
36 412 
36 377 

36 343 
36 308 
36 274 
36 239 
36 204 

36170 
36135 
36101 
36 066 
36 032 

35 997 
35 963 
35 928 
35 894 
35 860 

35 825 
35 791 
35 757 
35 722 
35 688 

35 654 
35 619 
35 585 
35 551 
35 517 

35 483 
35 448 
35 414 
35 380 
35 346 
35 312 
35 278 
35 244 
35 210 
35176 

35142 



9.96 403 
9.96 397 
9.96 392 
9.96 387 
9.96 381 

9.96 376 
9.96 370 
9.96 365 
9.96 360 
9.96 354 

9.96 349 
9.96 343 
9.96 338 
9.96 333 
9.96 327 

9.96 322 
9.96 316 
9.96 311 
9.96 305 
9.96 300 

9.96 294 
9.96 289 
9.96 284 
9.96 278 
9.96 273 

9.96 267 
9.96 262 
9.96 256 
9.96 251 
9.96 245 

9.96 240 
9.96 234 
9.96 229 
9.96 223 
9.96 218 
9.96 212 
9.96 207 
9.96 201 
9.96 196 
9.96 190 

9.96 185 
9.96179 
9.96 174 
9.96168 
9.96 162 

9.96 157 
9.96151 
9.96146 
9.96 140 
9.96135 

9.96 129 
9.96123 
9.96118 
9.96112 
9.96107 

9.96 101 
9.96 095 
9.96 090 
9.96 084 
9.96 079 

9.96 073 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





36 


2 


7.2 


3 


10.8 


4 


14.4 


5 


18.0 


6 


21.6 


7 


25.2 


8 


28.8 


9 


32.4 



34 

6.8 
10.2 
13.6 
17.0 
20.4 
23.8 
27.2 
30.6 





29 


2 


5.8 


3 


8.7 


4 


11.6 


5 


14.5 


6 


17.4 


7 


20.3 


8 


23.2 


9 


26.1 



6 

1.2 

1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



35 

7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 

30 

6.0 
9.0 
12.0 
lo.O 
18.0 
21.0 
24.0 
27.0 

28 

5.6 
8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 

5 

1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 



From the top: 

For23 o+ or203 o+ , 

read as printed ; for 
113° + or293°+ read 

co-function. 

From the bottom: 

For66° + or246°+ 
read as printed ; for 
156 0+ or336 0+ ,read 
co-function. 



LCos 



LCtn 



cd LTan LSin d ' 



Prop. Pts. 



66° — Logarithms of Trigonometric Functions 



70 



24° — Logarithms of Trigonometric Functions 



[in 



o 

i 

2 

3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 

42 
43 
44 

45 
46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 

58 
59 

60 



LSin 



9.60 931 
9.60 960 

9.60 988 
9.61016 

9.61 045 

9.61 073 
9.61 101 
9.61 129 
9.61 158 
9.61 186 

9.61 214 
9.61 242 
9.61 270 
9.61 298 
9.61 326 

9.61 354 
9.61 382 
9.61411 
9.61 438 
9.61 466 

9.61 494 
9.61 522 
9.61 550 
9.61 578 
9.61 606 

9.61 634 
9.61 662 
9.61 689 
9.61 717 
9.61 745 

9.61 773 
9.61 800 
9.61 828 
9.61 856 
9.61 883 

9.61 911 
9.61 939 
9.61 966 

9.61 994 

9.62 021 



62 049 
62 076 
62 104 
62 131 
62 159 

62 186 
62 214 
62 241 
62 268 
62 296 
62 323 
62 350 
62 377 
62 405 
62 432 

62 459 
62 486 
62 513 
62 541 
62 568 
62 595 



LCos 



29 

28 
28 
29 
28 

28 

28 
29 
28 
28 

28 

28 
28 
28 
28 

28 
29 
27 
28 
28 

28 

28 
28 
28 
28 

28 
27 
28 
28 
28 

27 

28 
28 
27 
28 

28 
27 
28 
27 
28 

27 
28 
27 
28 
27 

28 
27 
27 
28 
27 

27 
27 

28 
27 
27 

27 
27 
28 
27 
27 



LTan 



9.64 858 
9.64 892 
9.64 926 
9.64 960 

9.64 994 

9.65 028 
9.65 062 
9.65 096 
9.65 130 
9.65 164 

9.65 197 
9.65 231 
9.65 265 
9.65 299 
9.65 333 
9.65 366 
9.65 400 
9.65 434 
9.65 467 
9.65 501 

9.65 535 
9.65 568 
9.65 602 
9.65 636 
9.65 669 

9.65 703 
9.65 736 
9.65 770 
9.65 803 
9.65 837 

9.65 870 
9.65 904 
9.65 937 

9.65 971 

9.66 004 

9.66 038 
9.66 071 
9.66 104 
9.66 138 
9.66 171 

9.66 204 
9.66 238 
9.66 271 
9.66 304 
9.66 337 
9.66 371 
9.66 404 
9.66 437 
9.66 470 
9.66 503 

9.66 537 
9.66 570 
9.66 603 
9.66 636 
9.66 669 
9.66 702 
9.66 735 
9.66 768 
9.66 801 
9.66 834 

9.66 867 



LCtn 



cd LCtn LCos d 



34 
34 
34 
34 
34 

34 
34 
34 
34 
33 

34 
34 
34 
34 
33 

34 
34 
33 
34 
34 

33 
34 
34 
33 
34 

33 
34 
33 
34 
33 

34 
33 
34 
33 
34 

33 
33 
34 
33 
33 

34 
33 
33 
33 
34 

33 
33 
33 
33 
34 

33 
33 
33 
33 
33 

33 
33 
33 
33 
33 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10, 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10, 
10, 
10, 

10. 
10, 
10. 
10. 
10, 

10, 
10, 
10, 
10, 
10, 

10, 
10, 
10, 
10, 
10, 
10, 
10 
10, 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 
10 



35142 
35108 
35 074 
35 040 
35 006 

34 972 

34 938 
34 904 
34 870 
34 836 

34 803 
34 769 
34735 
34 701 
34 667 

34 634 
34 600 
34 566 
34 533 
34 499 

34465 
34432 
34 398 
34 364 
34 331 

34 297 
34 264 
34 230 
34197 
34163 
34130 
34 096 
34 063 
34 029 
33 996 

33 962 
33 929 
33 896 
33 862 
33 829 

33 796 
33 762 
33 729 
33 696 
33 663 

33 629 
33 596 
33 563 
33 530 
33 497 
33 463 
,33 430 
,33 397 
,33 364 
,33 331 

,33 298 
,33 265 
.33 232 
.33 199 
.33 166 
,33 133 



cd LTan 



9.96 073 
9.96 067 
9.96 062 
9.96 056 
9.96 050 

9.96 045 
9.96 039 
9.96 034 
9.96 028 
9.96 022 

9.96 017 
9.96 011 
9.96 005 
9.96 000 
9.95 994 

9.95 988 
9.95 982 
9.95 977 
9.95 971 
9.95 965 

9.95 960 
9.95 954 
9.95 948 
9.95 942 
9.95 937 

9.95 931 
9.95 925 
9.95 920 
9.95 914 
9.95 908 

9.95 902 
9.95 897 
9.95 891 
9.95 885 
9.95 879 
9.95 873 
9.95 868 
9.95 862 
9.95 856 
9.95 850 

9.95 844 
9.95 839 
9.95 833 
9.95 827 
9.95 821 

9.95 815 
9.95 810 
9.95 804 
9.95 798 
9.95 792 

9.95 786 
9.95 780 
9.95 775 
9.95 769 
9.95 763 

9.95 757 
9.95 751 
9.95 745 
9.95 739 
9.95 733 

9.95 728 



LSin d ' 



| Prop. Pts. 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 






34 


2 


6.8 


3 


10.2 


4 


13.6 


5 


17.0 


6 


20.4 


7 


23.8 


8 


27.2 


9 


30.6 





29 


2 


5.8 


3 


8.7 


4 


11.6 


5 


14.5 


6 


17.4 


7 


20.3 


8 


23.2 


9 


26.1 





27 


2 


5.4 


3 


8.1 


4 


10.8 


5 


13.5 


6 


16.2 


7 


18.9 


8 


21.6 


9 


24.3 



33 

6.6 
9.9 
13.2 
16.5 
19.8 
23.1 
26.4 
29.7 

28 

5.6 

8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 

6 

1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



5 

1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 



From the top: 
For24 o+ or204°+ 
read as printed; for 
114°+ or 294°+, read 
co-function. 

From the bottom: 
For65° + or245° + , 
read as printed; for 
155°+ or 335°+ read 
co-function. 



Prop. Pts, 



65° — Logarithms of Trigonometric Functions 



Ill] 25° — Logarithms of Trigonometric Functions 



71 



LSin 



LTan 



cd 



LCtn 



LCos 



Prop. Pts. 





1 
2 
3 
4 

5 

6 

7 
8 
9 

10 

11 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 
55 
56 
57 
58 
59 

60 



.62 595 
,62 622 
,62 649 
.62 676 
,62 703 

62 730 
62 757 
62 784 
62 811 
62 838 

62 865 
62 892 
62 918 
62 945 
62 972 

62 999 

63 026 
63 052 
63 079 
63 106 
63 133 
63 159 
63 186 
63 213 
63 239 

63 266 
63 292 
63 319 
63 345 
63 372 

63 398 
63 425 
63 451 
63 478 
63 504 

63 531 
63 557 
63 583 
63 610 
63 636 
63 662 
63 689 
63 715 
63 741 
63 767 
63 794 
63 820 
63 846 
63 872 
63 898 
63 924 
63 950 

63 976 

64 002 
64 028 
64 054 
,64 080 
64 106 
,64 132 
,64 158 

,64 184 



27 
27 
27 
27 
27 

27 
27 
27 
27 

27 

27 
26 
27 
27 
27 

27 

26 
27 
27 
27 

26 
27 
27 
26 
27 

26 
27 
26 
27 
26 

27 
26 
27 
26 
27 
26 
26 
27 
26 
26 

27 
26 
26 
26 
27 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 



9.66 867 
9.66 900 
9.66 933 
9.66 966 

9.66 999 

9.67 032 
9.67 065 
9.67 098 
9.67 131 
9.67 163 
9.67 196 
9.67 229 
9.67 262 
9.67 295 
9.67 327 

9.67 360 
9.67 393 
9.67 426 
9.67 458 
9.67 491 

9.67 524 
9.67 556 
9.67 589 
9.67 622 
9.67 654 
9.67 687 
9.67 719 
9.67 752 
9.67 785 
9.67 817 

9.67 850 
9.67 882 
9.67 915 
9.67 947 

9.67 980 

9.68 012 
9.68 044 
9.68 077 
9.68 109 
9.68 142 

9.68 174 
9.68 206 
9.68 239 
9.68 271 
9.68 303 
9.68 336 
9.68 368 
9.68 400 
9.68 432 
9.68 465 

9.68 497 
9.68 529 
9.68 561 
9.68 593 
9.68 626 

9.68 658 
9.68 690 
9.68 722 
9.68 754 
9.68 786 

9.68 818 



33 
33 
33 
33 
33 

33 
33 
33 
32 
33 

33 
33 
33 
32 
33 

33 
33 
32 
33 
33 

32 
33 
33 
32 
33 

32 
33 
33 
32 
33 

32 
33 
32 
33 
32 

32 
33 
32 
33 
32 

32 
33 
32 
32 
33 

32 
32 
32 
33 
32 

32 
32 
32 
33 
32 

32 

32 
32 
32 
32 



0.33 133 
0.33 100 
0.33 067 
0.33 034 
0.33 001 

0.32 968 
0.32 935 
0.32 902 
0.32 869 
0.32 837 

0.32 804 
0.32 771 
0.32 738 
0.32 705 
0.32 673 

0.32 640 
0.32 607 
0.32 574 
0.32 542 
0.32 509 

0.32 476 
0.32 444 
0.32 411 
0.32 378 
0.32 346 

0.32 313 
0.32 281 
0.32 248 
0.32 215 
0.32 183 

0.32 150 
0.32118 
0.32 085 
0.32 053 
0.32 020 

0.31 988 
0.31956 
0.31923 
0.31 891 
0.31 858 
0.31 826 
0.31 794 
0.31761 
0.31 729 
0.31 697 
0.31 664 
0.31 632 
0.31 600 
0.31 568 
0.31 535 

0.31 503 
0.31471 
0.31439 
0.31407 
0.31 374 
0.31 342 
0.31310 
0.31 278 
0.31 246 
0.31214 

10.31 182 



9.95 728 
9.95 722 
9.95 716 
9.95 710 
9.95704 

9.95 698 
9.95 692 
9.95 686 
9.95 680 
9.95 674 
9.95 668 
9.95 663 
9.95 657 
9.95 651 
9.95 645 

9.95 639 
9.95 633 
9.95 627 
9.95 621 
9.95 615 
9.95 609 
9.95 603 
9.95 597 
9.95 591 
9.95 585 
9.95 579 
9.95 573 
9.95 567 
9.95 561 
9.95 555 

9.95 549 
9.95 543 
9.95 537 
9.95 531 
9.95 525 

9.95 519 
9.95 513 
9.95 507 
9.95 500 
9.95 494 

9.95488 
9.95 482 
9.95 47a 
9.95 470 
9.95 464 

9.95 458 
9.95 452 
9.95 446 
9.95 440 
9.95 434 

9.95 427 
9.95 421 
9.95 415 
9.95409 
9.95 403 

9.95 397 
9.95 391 
9.95 384 
9.95 378 
9.95 372 

9.95 366 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 

38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 
14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





33 


2 


6.6 


3 


9.9 


4 


13.2 


5 


16.5 


6 


19.8 


7 


23.1 


8 


26.4 


9 


29.7 





27 


2 


5.4 


3 


8.1 


4 


10.8 


5 


13.5 


6 


16.2 


7 


18.9 


8 


21.6 


9 


24.3 





7 


2 


1.4 


3 


2.1 


4 


2.8 


5 


3.5 


6 


4.2 


7 


4.9 


8 


5.6 


9 


6.3 



32 

6.4 
9.6 
12.8 
16.0 
19.2 
22.4 
25.6 
28.8 

26 

5.2 

7.8 
10.4 
13.0 
15.6 
18.2 
20.8 
23.4 

6 

1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 



From the top: 

For25 o+ or205 o+ , 
read as printed; for 
115 0+ or295 0+ ,read 
co-function. 

From the bottom: 
For 64°+ or 244°+ 
read as printed; for 
154 0+ or334 0+ ,read 
co-function. 



LCos d 



LCtn 



cd 



L Tan L Sin d 



Prop. Pts. 



64° — Logarithms of Trigonometric Functions 



72 



26° — Logarithms of Trigonometric Functions 



[HI 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.64 184 
9.64 210 
9.64 236 
9.64 262 
9.64 288 

9.64 313 
9.64 339 
9.64 365 
9.64 391 
9.64 417 
9.64 442 
9.64 468 
9.64 494 
9.64 519 
9.64 545 

9.64 571 
9.64 596 
9.64 622 
9.64 647 
9.64 673 

9.64 698 
9.64 724 
9.64 749 
9.64 775 
9.64 800 

9.64 826 
9.64 851 
9.64 877 
9.64 902 
9.64 927 

9.64 953 

9.64 978 

9.65 003 
9.65 029 
9.65 054 
9.65 079 
9.65 104 
9.65 130 
9.65 155 
9.65 180 
9.65 205 
9.65 230 
9.65 255 
9.65 281 
9.65 306 

9.65 331 
9.65 356 
9.65 381 
9.65 406 
9.65 431 



.65 456 
.65 481 
.65 506 
.65 531 
.65 556 

.65 580 
.65 605 
.65 630 
.65 655 
.65 680 

.65 705 



LCos 



26 
26 
26 
26 
25 

26 

26 
26 
26 
25 

26 

26 
25 
26 
26 

25 
25 
25 
26 
25 

26 
25 
26 
25 
26 

25 
26 
25 
25 
26 

25 
25 
26 
25 
25 

25 

26 
25 
25 
25 

25 
25 
26 
25 
25 

25 
25 
25 
25 
25 

25 
25 
25 
25 
24 

25 
25 
25 
25 
25 



LTan cd 



9.68 818 
9.68 850 
9.68 882 
9.68 914 
9.68 946 

9.68 978 

9.69 010 
9.69 042 
9.69 074 
9.69 106 

9.69 138 
9.69 170 
9.69 202 
9.69 234 
9.69 266 

9.69 298 
9.69 329 
9.69 361 
9.69 393 
9.69 425 

9.69 457 
9.69 488 
9.69 520 
9.69 552 
9.69 584 

9.69 615 
9.69 647 
9.69 679 
9.69 710 
9.69 742 

9.69 774 
9.69 805 
9.69 837 
9.69 868 
9.69 900 

9.69 932 
9.69 963 

9.69 995 

9.70 026 
9.70 058 

9.70 089 
9.70 121 
9.70 152 
9.70 184 
9.70 215 
9.70 247 
9.70 278 
9.70 309 
9.70 341 
9.70 372 

9.70 404 
9.70 435 
9.70 466 
9.70 498 
9.70 529 
9.70 560 
9.70 592 
9.70 623 
9.70 654 
9.70 685 

9.70 717 



LCtn cd 



32 
32 
32 
32 
32 

32 
32 
32 
32 
32 

32 
32 
32 
32 
32 

31 

32 
32 
32 
32 

31 

32 
32 
32 
31 

32 
32 
31 
32 
32 

31 

32 
31 
32 
32 

31 

32 
31 
32 
31 

32 
31 
32 
31 
32 

31 

31 
32 
31 
32 

31 

31 
32 
31 
31 

32 
31 
31 
31 
32 



L Ctn L Cos d 



10.31 182 
10.31 150 
10.31118 
10.31 086 
10.31 054 

10.31 022 
10.30 990 
10.30 958 
10.30 926 
10.30 894 
10.30 862 
10.30 830 
10.30 798 
10.30 766 
10.30 734 

10.30 702 
10.30 671 
10.30 639 
10.30 607 
10.30 575 

10.30 543 
10.30 512 
10.30480 
10.30448 
10.30416 

10.30 385 
10.30 353 
10.30 321 
10.30 290 
10.30 258 

10.30 226 
10.30 195 
10.30163 
10.30132 
10.30 100 

10.30 068 
10.30 037 
10.30 005 
10.29 974 
10.29 942 

10.29 911 
10.29 879 
10.29 848 
10.29 816 
10.29 785 

10.29 753 
10.29 722 
10.29 691 
10.29 659 
10.29 628 

10.29 596 
10.29 565 
10.29 534 
10.29 502 
10.29 471 

10.29 440 
10.29 408 
10.29 377 
10.29 346 
10.29 315 
10.29 283 



9.95 366 
9.95 360 
9.95 354 
9.95 348 
9.95 341 

9.95 335 
9.95 329 
9.95 323 
9.95 317 
9.95 310 

9.95 304 
9.95 298 
9.95 292 
9.95 286 
9.95 279 

9.95 273 
9.95 267 
9.95 261 
9.95 254 
9.95 248 

9.95 242 
9.95 236 
9.95 229 
9.95 223 
9.95 217 
9.95 211 
9.95 204 
9.95 198 
9.95 192 
9.95 185 

9.95 179 
9.95 173 
9.95 167 
9.95 160 
9.95 154 

9.95 148 
9.95 141 
9.95 135 
9.95 129 
9.95 122 

9.95116 
9.95 110 
9.95 103 
9.95 097 
9.95 090 
9.95 084 
9.95 078 
9.95 071 
9.95 065 
9.95 059 
9.95 052 
9.95 046 
9.95 039 
9.95 033 
9.95 027 

9.95 020 
9.95 014 
9.95 007 
9.95 001 
9.94 995 

9.94 988 



LTan LSin d 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 
14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 





32 


2 


6.4 


3 


9.6 


4 


12.8 


5 


16.0 


6 


19.2 


7 


22.4 


8 


25.6 


9 


28.8 





26 


2 


5.2 


3 


7.8 


4 


10.4 


5 


13.0 


6 


15.6 


7 


18.2 


8 


20.8 


9 


23.4 





24 


2 


4.8 


3 


7.2 


4 


9.6 


5 


12.0 


6 


14.4 


7 


16.8 


8 


19.2 


9 


21.6 



31 

6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

25 

5.0 
7.5 
10.0 
12.5 
15.0 
17.5 
20.0 
22.5 

7 

1.4 
2.1 

2.8 
3.5 
4.2 
4.9 
5.6 
6.3 



6 

1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



From the top: 

For26 o+ or206 o+ , 

read as printed; for 
116° + or296° + ,read 
co-function. 

From the bottom: 

For63° + or243° + , 
read as printed; for 
153° + or333° + ,read 
co-function. 



Prop. Pts. 



63° — Logarithms of Trigonometric Functions 



Ill] 27° — Logarithms of Trigonometric Functions 



73 



' LSin 





1 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 

42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



9.65 
9.65 
9.65 
9.65 
9.65 

9.65 
9.65 
9.65 
9.65 
9.65 
9.65 
9.65 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.66 

9.66 
9.66 
9.66 
9.66 
9.67 

9.67 
9.67 
9.67 
9.67 
9.67 
9.67 



705 
729 
754 

779 
804 

828 
853 
878 
902 
927 
952 
976 
001 
025 
050 

075 
099 
124 
148 
173 

197 
221 
246 
270 
295 

319 
343 
368 
392 
416 
441 
465 
489 
513 
537 
562 
586 
610 
634 
658 
682 
706 
731 
755 
779 

803 
827 
851 
875 
899 
922 
946 
970 
994 
018 

042 
066 
090 
113 
137 

161 



LCos d 



24 
25 
25 
25 
24 

25 
25 
24 
25 
25 

24 
25 
24 
25 
25 
24 
25 
24 
25 
24 

24 
25 
24 
25 
24 

24 
25 
24 
24 
25 

24 
24 
24 
24 
25 

24 

24 
24 
24 
24 
24 
25 
24 
24 
24 

24 
24 
24 
24 
23 

24 
24 
24 
24 
24 

24 
24 
23 
24 
24 



LTan cd L Ctn LCos d 



9.70 717 

9.70 748 
9.70 779 
9.70 810 
9.70 841 

9.70 873 
9.70 904 
9.70 935 
9.70 966 

9.70 997 

9.71 028 
9.71 059 
9.71 090 
9.71 121 
9.71 153 

9.71 184 
9.71215 
9.71 246 
9.71277 
9.71 308 

9.71 339 
9.71 370 
9.71 401 
9.71 431 
9.71 462 

9.71 493 
9.71 524 
9.71 555 
9.71 586 
9.71 617 

9.71 648 
9.71 679 
9.71 709 
9.71 740 
9.71 771 
9.71 802 
9.71 833 
9.71 863 
9.71 894 
9.71 925 
9.71 955 

9.71 986 

9.72 017 
9.72 048 
9.72 078 

9.72 109 
9.72 140 
9.72 170 
9.72 201 
9.72 231 

9.72 262 
9.72 293 
9.72 323 
9.72 354 
9.72 384 

9.72 415 

9.72 445 
9.72 476 
9.72 506 
9.72 537 

9.72 567 



LCtn 



31 
31 
31 
31 
32 

31 

31 
31 
31 
31 

31 
31 
31 
32 
31 

31 

31 
31 
31 
31 

31 
31 
30 
31 
31 

31 
31 
31 
31 
31 

31 
30 
31 
31 
31 
31 
30 
31 
31 
30 

31 
31 
31 
30 
31 

31 
30 
31 
30 
31 

31 

30 
31 
30 
31 

30 
31 
30 
31 
30 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10, 
10. 
10, 
10. 

10, 
10, 
10, 
10, 
10, 

10, 
10 
10 
10 
10 

10 
10 
10 
10 
10, 

10, 
10, 
10, 
10, 
10 

10, 
10, 
10 
10 
10, 

10 



29 283 
29 252 
29 221 
29190 
29159 

29127 
29 096 
29 065 
29 034 
29 003 
28 972 
28 941 
28 910 
28 879 
28 847 

28 816 

28 785 
28 754 
28 723 
28 692 

28 661 
28 630 
,28 599 
28 569 

28 538 

28507 
,28476 
,28445 
,28414 
,28 383 

,28 352 
,28 321 
,28 291 
,28 260 
.28 229 

.28 198 
.28 167 
.28137 
.28 106 
.28 075 

.28 045 

.28 014 
.27 983 
.27 952 
.27 922 

.27 891 
.27 860 
.27 830 
.27 799 
.27769 

,27 738 
.27707 
.27 677 
.27 646 
.27 616 

.27 585 
.27555 
.27 524 
.27494 
.27463 
.27433 



cd LTan LSin d 



9.94 988 
9.94 982 
9.94 975 
9.94 969 
9.94 962 

9.94 956 
9.94 949 
9.94 943 
9.94 936 
9.94 930 
9.94 923 
9.94 917 
9.94 911 
9.94 904 
9.94 898 
9.94 891 
9.94 885 
9.94 878 
9.94 871 
9.94865 

9.94858 
9.94 852 
9.94 845 
9.94 839 
9.94 832 

9.94 826 
9.94 819 
9.94 813 
9.94 806 
9.94 799 

9.94 793 
9.94 786 
9.94 780 
9.94 773 
9.94 767 

9.94 760 
9.94 753 
9.94 747 
9.94 740 
9.94 734 

9.94 727 
9.94 720 
9.94 714 
9.94 707 
9.94 700 

9.94 694 
9.94 687 
9.94 680 
9.94 674 
9.94 667 

9.94 660 
9.94 654 
9.94 647 
9.94 640 
9.94 634 

9.94 627 
9.94 620 
9.94 614 
9.94 607 
9.94 600 

9.94 593 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 

42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 

2 
1 





Prop. Pts. 





32 


2 


6.4 


3 


9.6 


4 


12.8 


5 


16.0 


6 


19.2 


7 


22.4 


8 


25.6 


9 


28.8 





30 


2 


6.0 


3 


9.0 


4 


12.0 


5 


15.0 


6 


18.0 


7 


21.0 


8 


24.0 


9 


27.0 



31 

6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

25 

5.0 
7.5 
10.0 
12.5 
15.0 
17.5 
20.0 
22.5 

23 

4.6 
6.9 
9.2 
11.5 
13.8 
16.1 
18.4 
20.7 

6 

1.2 

1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



From the top: 

For27 o+ or207°+ 
read as printed; for 
117 0+ or297 0+ ,read 
co-function. 

From the bottom: 

For62 0+ or242 0+ , 
read as printed; for 
152 0+ or332 0+ ,read 
co-function. 





24 


2 


4.8 


3 


7.2 


4 


9.6 


5 


12.0 


6 


14.4 


7 


16.8 


8 


19.2 


9 


21.6 





7 


2 


1.4 


3 


2.1 


4 


2.8 


5 


3.5 


6 


4.2* 


7 


4.9 


8 


5.6 


9 


6.3 



Prop. Pts. 



62° — Logarithms of Trigonometric Functions 



74 



28° — Logarithms of Trigonometric Functions [III 



LSin 



d LTan cd 



L Ctn L Cos d 



Prop. Pts. 





1 
2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 



9.67 161 
9.67 185 
9.67 208 
9.67 232 
9.67 256 

9.67 280 
9.07 303 
9.67 327 
9.67 350 
9.67 374 

9.67 398 
9.67 421 
9.67 445 
9.67 468 
9.67 492 

9.67 515 
9.67 539 
9.67 562 
9.67 586 
9.67 609 

9.67 633 
9.67 656 
9.67 680 
9.67 703 
9.67 726 
9.67 750 
9.67 773 
9.67 796 
9.67 820 
9.67 843 

9.67 866 
9.67 890 
9.67 913 
9.67 936 
9.67 959 

9.67 982 

9.68 006 
9.68 029 
9.68 052 
9.68075 

9.68 098 
9.68 121 
9.68 144 
9.68 167 
9.68 190 



68 213 
68 237 
68 260 
,68 283 
,68 305 

,68 328 
,68 351 
.68 374 
.68 397 
.68 420 



9.68 443 
9.68 466 
9.68 489 
9.68 512 
9.68 534 

9.68 557 



24 
23 
24 
24 
24 

23 

24 
23 
24 
24 

23 

24 
23 
24 
23 

24 
23 
24 
23 
24 

23 
24 
23 
23 
24 

23 

23 
24 
23 
23 

24 
23 
23 
23 
23 

24 
23 
23 
23 
23 

23 

23 
23 
23 
23 

24 
23 
23 
22 
23 

23 
23 
23 
23 
23 

23 
23 
23 
22 
23 



72 567 
72 598 
72 628 
72 659 
72 689 

72 720 

72 750 
72 780 
72 811 
72 841 

72 872 
72 902 
72 932 
72 963 

72 993 

73 023 
73 054 
73 084 
73114 
73 144 

73 175 

73 205 
73 235 
73 265 
73 295 

73 326 
73 356 
73 386 
73 416 
73 446 

73 476 
73 507 
73 537 
73 567 
73 597 

73 627 
73 657 
73 687 
73 717 
73 747 

73 777 
73 807 
73 837 
73 867 
73 897 
73 927 
73 957 

73 987 

74 017 
74 047 

74 077 
74 107 
74 137 
74 166 
74 196 

74 226 

74 256 
74 286 
74 316 
,74 345 
74 375 



31 

30 
31 
30 
31 

30 
30 
31 
30 
31 

30 
30 
31 
30 
30 

31 

30 
30 
30 
31 

30 
30 
30 
30 
31 

30 
30 
30 
30 
30 

31 

30 
30 
30 
30 

30 
30 
30 
30 
30 

30 
30 
30 
30 
30 

30 
30 
30 
30 
30 

30 
30 
29 
30 
30 

30 
30 
30 
29 
30 



0.27433 
0.27402 
0.27 372 
0.27 341 
0.27 311 

0.27 280 
0.27 250 
0.27 220 
0.27 189 
0.27 159 

0.27 128 
0.27 098 
0.27 068 
0.27 037 
0.27 007 

0.26 977 
0.26 946 
0.26 916 
0.26 886 
0.26 856 

0.26 825 
0.26 795 
0.26 765 
0.26 735 
0.26 705 

0.26 674 
0.26 644 
0.26 614 
0.26 584 
0.26 554 

0.26 524 
0.26 493 
0.26463 
0.26 433 
0.26 403 

0.26 373 
0.26 343 
0.26 313 
0.26 283 
0.26 253 

0.26 223 
0.26 193 
0.26 163 
0.26 133 
0.26 103 

0.26 073 
0.26 043 
0.26 013 
0.25 983 
0.25 953 

0.25 923 
0.25 893 
0.25 863 
0.25 834 
0.25 804 
0.25 774 
0.25 744 
0.25 714 
0.25 684 
0.25 655 

10.25 625 



9.94 593 
9.94 587 
9.94 580 
9.94 573 
9.94 567 
9.94 560 
9.94 553 
9.94 546 
9.94 540 
9.94 533 
9.94 526 
9.94 519 
9.94 513 
9.94 506 
9.94499 
9.94 492 
9.94485 
9.94479 
9.94472 
9.94465 

9.94 458 
9.94 451 
9.94 445 
9.94 438 
9.94431 
9.94 424 
9.94417 
9.94410 
9.94 404 
9.94 397 
9.94 390 
9.94 383 
9.94 376 
9.94 369 
9.94 362 

9.94 355 
9.94 349 
9.94 342 
9.94 335 
9.94 328 

9.94 321 
9.94 314 
9.94 307 
9.94 300 
9.94 293 

9.94 286 
9.94 279 
9.94 273 
9.94 266 
9.94 259 

9.94 252 
9.94 245 
9.94 238 
9.94 231 
9.94 224 

9.94 217 
9.94 210 
9.94 203 
9.94 196 
9.94 189 
9.94 182 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 







31 


2 


6.2 


3 


9.3 


4 


12.4 


5 


15.5 


6 


18.6 


7 


21.7 


8 


24.8 


9 


27.9 





29 


2 


5.8 


3 


8.7 


4 


11.6 


5 


14.5 


6 


17.4 


7 


20.3 


8 


23.2 


9 


26.1 



30 

6.0 
9.0 
12.0 
15.0 
18.0 
21.0 
24.0 
27.0 

24 

4.8 
7.2 
9.6 
12.0 
14.4 
16.8 
19.2 
21.6 

22 

4.4 
6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 

6 

1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 



From the top: 

For28 o+ or208 o+ , 
read as printed; for 
118 0+ or298 0+ ,read 

co-function. 

From the bottom: 
For61 0+ or241 0+ , 
read as printed ; for 
151° + or331°+ read 
co-function. 





23 


2 


4.6 


3 


6.9 


4 


9.2 


5 


11.5 


6 


13.8 


7 


16.1 


8 


18.4 


9 


20.7 





7 


2 


1.4 


3 


2.1 


4 


2.8 


5 


3.5 


6 


4.2 


7 


4.9 


8 


5.6 


9 


6.3 



LCos 



L Ctn c d 



LTan LSin d ' 



Prop. Pts. 



61° — Logarithms of Trigonometric Functions 



Ill] 29° — Logarithms of Trigonometric Functions 



75 



LSin 



LTan cd 



LCtn 



LCos d 



Prop. Pts. 



7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



9.68 
9.68 
9.68 
9.68 
9.68 

9.68 
9.68 
9.68 
9.68 
9.68 

9.68 
9.68 
9.68 
9.68 
9.68 

9.68 
9.68 
9.68 
9.68 
9.68 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 
9.69 
9.69 
9.69 
9.69 

9.69 



557 

580 
603 
625 
648 

671 
694 
716 
739 

762 

784 
807 
829 
852 

875 

897 
920 
942 
965 

987 

010 
032 
055 
077 
100 

122 
144 
167 
189 
212 

234 
256 
279 
301 
323 

345 

368 
390 
412 
434 

456 
479 
501 
523 
545 

567 
589 
611 
633 
655 

677 

699 
721 
743 

765 

787 
809 
831 
853 

875 

897 



23 
23 
22 
23 
23 

23 

22 
23 
23 
22 

23 

22 
23 
23 

22 

23 

22 
23 
22 
23 

22 
23 
22 
23 
22 

22 
23 
22 
23 
22 

22 

23 
22 
22 
22 

23 

22 

22 
22 
22 

23 

22 
22 
22 
22 

22 
22 
22 
22 
22 

22 

22 
22 
22 
22 

22 
22 
22 
22 
22 



9.74 375 
9.74 405 
9.74 435 
9.74 465 
9.74 494 

9.74 524 
9.74 554 
9.74 583 
9.74 613 
9.74 643 

9.74 673 
9.74 702 
9.74 732 
9.74 762 
9.74 791 

9.74 821 
9.74 851 
9.74 880 
9.74 910 
9.74 939 

9.74 969 

9.74 998 

9.75 028 
9.75 058 
9.75 087 

9.75 117 
9.75 146 
9.75 176 
9.75 205 
9.75 235 

9.75 264 
9.75 294 
9.75 323 
9.75 353 
9.75 382 

9.75 411 
9.75 441 
9.75 470 
9.75 500 
9.75 529 

9.75 558 
9.75 588 
9.75 617 
9.75 647 
9.75 676 

9.75 705 
9.75 735 
9.75 764 
9.75 793 
9.75 822 

9.75 852 
9.75 881 
9.75 910 
9.75 939 
9.75 969 

9.75 998 

9.76 027 
9.76 056 
9.76 086 
9.76 115 

9.76 144 



30 
30 
30 
29 
30 

30 
29 
30 
30 
30 

29 
30 
30 
29 
30 

30 
29" 
30 
29 
30 

29 
30 
30 
29 
30 

29 
30 
29 
30 
29 

30 
29 
30 
29 
29 

30 
29 
30 
29 
29 

30 
29 
30 
29 
29 

30 
29 
29 
29 
30 

29 
29 
29 
30 
29 

29 
29 
30 
29 
29 



10.25 625 
10.25 595 
10.25 565 
10.25 535 
10.25 506 

10.25 476 
10.25 446 
10.25 417 
10.25 387 
10.25 357 

10.25 327 
10.25 298 
10.25 268 
10.25 238 
10.25 209 

10.25 179 
10.25 149 
10.25 120 
10.25 090 
10.25 061 

10.25 031 
10.25 002 
10.24 972 
10.24 942 
10.24 913 

10.24 883 
10.24 854 
10.24 824 
10.24 795 
10.24 765 

10.24 736 
10.24 706 
10.24 677 
10.24 647 
10.24 618 

10.24 589 
10.24 559 
10.24 530 
10.24 500 
10.24 471 
10.24 442 
10.24412 
10.24 383 
10.24 353 
10.24 324 

10.24 295 
10.24 265 
10.24 236 
10.24 207 
10.24 178 

10.24 148 
10.24119 
10.24 090 
10.24 061 
10.24 031 
10.24 002 
10.23 973 
10.23 944 
10.23 914 
10.23 885 
10.23 856 



9.94 182 
9.94 175 
9.94 168 
9.94 161 
9.94 154 

9.94 147 
9.94 140 
9.94 133 
9.94 126 
9.94119 
9.94112 
9.94 105 
9.94 098 
9.94 090 
9.94 083 

9.94 076 
9.94 069 
9.94 062 
9.94 055 
9.94 048 

9.94 041 
9.94 034 
9.94 027 
9.94 020 
9.94 012 

9.94 005 
9.93 998 
9.93 991 
9.93 984 
9.93 977 

9.93 970 
9.93 963 
9.93 955 
9.93 948 
9.93 941 

9.93 934 
9.93 927 
9.93 920 
9.93 912 
9.93 905 

9.93 898 
9.93 891 
9.93 884 
9.93 876 
9.93 809 

9.93 862 
9.93 855 
9.93 847 
9.93 840 
9.93 833 

9.93 826 
9.93 819 
9.93 811 
9.93 804 
9.93 797 

9.93 789 
9.93 782 
9.93 775 
9.93 768 
9.93 760 

9.93 753 



60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 






30 


29 


2 


6.0 


5.8 


3 


9.0 


8.7 


4 


12.0 


11.6 


5 


15.0 


14.5 


6 


18.0 


17.4 


7 


21.0 


20.3 


8 


24.0 


23.2 


9 


27.0 


26.1 




23 


22 


2 


4.6 


4.4 


3 


6.9 


6.6 


4 


9.2 


8.8 


5 


11.5 


11.0 


6 


13.8 


13.2 


7 


16.1 


15.4 


8 


18.4 


17.6 


9 


20.7 


19.8 




8 


7 


2 


1.6 


1.4 


3 


2.4 


2.1 


4 


3.2 


2.8 


5 


4.0 


3.5 


6 


4.8 


4.2 


7 


5.6 


4.9 


8 


6.4 


5.6 


9 


7.2 


6.3 



From the top: 
For 29°+ or 209°+ 

read as printed; for 
119° + or299° + ,read 
co-function. 

From the bottom: 

For60 o+ or240 o+ , 
read as printed; for 
150 o+ or330 o+ ,read 
co-function. 



LCos d 



LCtn cd 



LTan 



LSin d 



Prop. Pts. 



60° — Logarithms of Trigonometric Functions 



76 



30° — Logarithms of Trigonometric Functions 



[III 



LSin 





1 
2 
3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 
47 

48 
49 

50 

51 

52 
53 
54 

55 

56 
57 
58 
59 

60 



69 897 
69 919 
69 941 
69 963 

69 984 

70 006 
70 028 
70 050 
70 072 
70 093 

70115 
70137 
70 159 
70 180 
70 202 
70 224 
70 245 
70 267 
70 288 
70 310 
70 332 
70 353 
70 375 
70 396 
70 418 

70 439 
70 461 
70 482 
70 504 
70 525 

70 547 
70 568 
70 590 
70 611 
70 633 

70 654 
70 675 
70 697 
70 718 
70 739 

70 761 
70 782 
70 803 
70 824 
70 846 

70 867 
70 888 
70 909 
70 931 
70 952 

70 973 

70 994 
71015 
71036 
71058 

71079 

71 100 
71 121 
71 142 
,71 163 
71 184 



LCos d 



22 
22 
22 
21 
22 

22 
22 
22 
21 
22 

22 
22 
21 
22 
22 

21 

22 
21 
22 
22 

21 
22 
21 
22 
21 

22 

21 
22 
21 
22 

21 
22 
21 
22 
21 

21 

22 
21 
21 
22 

21 

21 
21 
22 
21 

21 

21 
22 
21 
21 

21 
21 
21 
22 
21 

21 
21 
21 
21 
21 



LTan cd 



9.76 144 
9.76 173 
9.76 202 
9.76 231 
9.76 261 

9.76 290 
9.76 319 
9.76 348 
9.76 377 
9.76 406 

9.76 435 
9.76 464 
9.76 493 
9.76 522 
9.76 551 

9.76 580 
9.76 609 
9.76 639 
9.76 668 
9.76 697 

9.76 725 
9.76 754 
9.76 783 
9.76 812 
9.76 841 

9.76 870 
9.76 899 
9.76 928 
9.76 957 

9.76 986 

9.77 015 
9.77 044 
9.77 073 
9.77 101 
9.77 130 

9.77 159 
9.77 188 
9.77 217 
9.77 246 
9.77 274 

9.77 303 
9.77 332 
9.77 361 
9.77 390 
9.77 418 

9.77 447 
9.77 476 
9.77 505 
9.77 533 
9.77 562 

9.77 591 
9.77 619 
9.77 648 
9.77 677 
9.77 706 

9.77 734 
9.77 763 
9.77 791 
9.77 820 
9.77 849 
9.77 877 



LCtn cd 



29 
29 
29 
30 
29 

29 
29 
29 
29 
29 

29 
29 
29 
29 
29 

29 
30 
29 
29 

28 

29 
29 
29 
29 
29 

29 
29 
29 
29 
29 

29 
29 
28 
29 
29 

29 
29 
29 
28 
29 

29 

29 
29 
28 
29 

29 
29 
28 
29 
29 

28 
29 
29 
29 
28 

29 
28 
29 
29 
28 



L Ctn L Cos d 



0.23 856 
0.23 827 
0.23 798 
0.23 769 
0.23 739 

0.23 710 
0.23 681 
0.23 652 
0.23 623 
0.23 594 

0.23 565 
0.23 536 
0.23 507 
0.23 478 
0.23 449 

0.23 420 
0.23 391 
0.23 361 
0.23 332 
0.23 303 

0.23 275 
0.23 246 
0.23 217 
0.23 188 
0.23 159 

0.23 130 
0.23 101 
0.23 072 
0.23 043 
0.23 014 

0.22 985 
0.22 956 
0.22 927 
0.22 899 
0.22 870 

0.22 841 
0.22 812 
0.22 783 
0.22 754 
0.22 726 

0.22 697 
0.22 668 
0.22 639 
0.22 610 
0.22 582 

0.22 553 
0.22 524 
0.22 495 
0.22 467 
0.22 438 

0.22 409 
0.22 381 
0.22 352 
0.22 323 
0.22 294 

0.22 266 
0.22 237 
0.22 209 
0.22 180 
0.22151 
10.22 123 



9.93 753 
9.93 746 
9.93 738 
9.93 731 
9.93 724 

9.93 717 
9.93 709 
9.93 702 
9.93 695 
9.93 687 
9.93 680 
9.93 673 
9.93 665 
9.93 658 
9.93 650 

9.93 643 
9.93 636 
9.93 628 
9.93 621 
9.93 614 

9.93 606 
9.93 599 
9.93 591 
9.93 584 
9.93 577 

9.93 569 
9.93 562 
9.93 554 
9.93 547 
9.93 539 

9.93 532 
9.93 525 
9.93 517 
9.93 510 
9.93 502 

9.93 495 
9.93 487 
9.93 480 
9.93 472 
9.93 465 

9.93 457 
9.93 450 
9.93 442 
9.93 435 
9.93 427 

9.93 420 
9.93 412 
9.93 405 
9.93 397 
9.93 390 

9.93 382 
9.93 375 
9.93 367 
9.93 360 
9.93 352 

9.93 344 
9.93 337 
9.93 329 
9.93 322 
9.93 314 

9.93 307 



L Tan L Sin d 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 

7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 





30 


29 


2 


6.0 


.5.8 


3 


9.0 


8.7 


4 


12.0 


11.6 


5 


15.0 


14.5 


6 


18.0 


17.4 


7 


21.0 


20.3 


8 


24.0 


23.2 


9 


27.0 


26.1 





28 


2 


5.6 


3 


8.4 


4 


11.2 


5 


14.0 


6 


16.8 


7 


19.6 


8 


22.4 


9 


25.2 





21 


2 


4.2 


3 


6.3 


4 


8.4 


5 


10.5 


6 


12.6 


7 


14.7 


8 


16.8 


9 


18.9 



22 

4.4 
6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 

8 

1.6 
2.4 
3.2 

4.0 
4.8 
5.6 
6.4 

7.2 





7 


2 


1.4 


3 


2.1 


4 


2.8 


5 


3.5 


6 


4.2 


7 


4.9 


8 


5.6 


9 


6.3 


From the top: 


For30 o+ or210 o+ , 


read as printed; for 


120 o+ or300 o+ ,read 


co-functi 


on. 



From the bottom: 

For 59°+ or 239°+ 
read as printed ; for 
149°+ or 329°+ read 

co-function. 



Prop. Pts. 



59° — Logarithms of Trigonometric Functions 



Ill] 31° — Logarithms of Trigonometric Functions 



77 



LSin 



LTan cd 



L Ctn L Cos d 



Prop. Pts. 





1 
2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 
46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 
9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 

9.71 
9.71 
9.71 
9.71 
9.71 
9.72 
9.72 
9.72 
9.72 
9.72 

9.72 
9.72 
9.72 
9.72 
9.72 
9.72 
9.72 
9.72 
9.72 
9.72 

9.72 
9.72 
9.72 
9.72 
9.72 
9.72 



184 
205 
226 
247 
268 

289 
310 
331 
352 
373 

393 
414 
435 
456 
477 
498 
519 
539 
560 
581 

602 
622 
643 
664 
685 

705 
726 

747 
767 
788 

809 
829 
850 
870 
891 

911 
932 
952 
973 
994 

014 
034 
055 
075 
096 

116 
137 
157 
177 
198 

218 
238 
259 
279 
299 

320 
340 
360 
381 
401 
421 



21 
21 
21 
21 
21 

21 
21 
21 
21 
20 

21 
21 
21 
21 
21 
21 
20 
21 
21 
21 

20 
21 
21 
21 
20 
21 
21 
20 
21 
21 

20 
21 
20 
21 
20 
21 
20 
21 
21 
20 

20 
21 
20 
21 
20 

21 
20 
20 
21 
20 

20 
21 
20 
20 
21 

20 
20 
21 
20 
20 



9.77 877 
9.77 906 
9.77 935 
9.77 963 

9.77 992 

9.78 020 
9.78 049 
9.78 077 
9.78 106 
9.78 135 

9.78 163 
9.78 192 
9.78 220 
9.78 249 
9.78 277 

9.78 306 
9.78 334 
9.78 363 
9.78 391 
9.78 419 

9.78 448 
9.78 476 
9.78 505 
9.78 533 
9.78 562 

9.78 590 
9.78 618 
9.78 647 
9.78 675 
9.78 704 

9.78 732 
9.78 760 
9.78 789 
9.78 817 
9.78 845 

9.78 874 
9.78 902 
9.78 930 
9.78 959 

9.78 987 

9.79 015 
9.79 043 
9.79 072 
9.79 100 
9.79 128 

9.79 156 
9.79 185 
9.79 213 
9.79 241 
9.79 269 

9.79 297 
9.79 326 
9.79 354 
9.79 382 
9.79 410 

9.79 438 
9.79 466 
9.79 495 
9.79 523 
9.79 551 

9.79 579 



29 
29 
28 
29 

28 

29 

28 
29 
29 
28 

29 

28 
29 
28 
29 

28 
29 
28 
28 
29 

28 
29 

28 
29 
28 

28 
29 
28 
29 
28 

28 
29 
28 
28 
29 

28 
28 
29 
28 
28 

28 
29 

28 
28 
28 

29 

28 
28 
28 
28 

29 

28 
28 
28 
28 

28 
29 

28 
28 
28 



0.22 123 
0.22 094 
0.22 065 
0.22 037 
0.22 008 

0.21 980 
0.21951 
0.21 923 
0.21 894 
0.21 865 

0.21 837 
0.21 808 
0.21 780 
0.21751 
0.21 723 

0.21 694 
0.21 666 
0.21 637 
0.21 609 
0.21 581 

0.21 552 
0.21 524 
0.21 495 
0.21 467 
0.21 438 

0.21410 
0.21 382 
0.21 353 
0.21 325 
0.21 296 

0.21 268 
0.21 240 
0.21211 
0.21 183 
0.21 155 

0.21 126 
0.21 098 
0.21 070 
0.21 041 
0.21 013 

0.20985 
0.20 957 
0.20 928 
0.20900 
0.20 872 

0.20 844 
0.20 815 
0.20787 
0.20759 
0.20731 

0.20 703 
0.20 674 
0.20 646 
0.20618 
0.20 590 
0.20 562 
0.20534 
0.20 505 
0.20 477 
0.20449 
10.20421 



9.93 307 
9.93 299 
9.93 291 
9.93 284 
9.93 276 
9.93 269 
9.93 261 
9.93 253 
9.93 246 
9.93 238 

9.93 230 
9.93 223 
9.93 215 
9.93 207 
9.93 200 

9.93 192 
9.93 184 
9.93 177 
9.93 169 
9.93 161 

9.93 154 
9.93 146 
9.93 138 
9.93 131 
9.93 123 

9.93 115 
9.93 108 
9.93 100 
9.93 092 
9.93 084 

9.93 077 
9.93 069 
9.93 061 
9.93 053 
9.93 046 
9.93 038 
9.93 030 
9.93 022 
9.93 014 
9.93 007 
9.92 999 
9.92 991 
9.92 983 
9.92 976 
9.92 968 

9.92 960 
9.92 952 
9.92 944 
9.92 936 
9.92 929 

9.92 921 
9.92 913 
9.92 905 
9.92 897 
9.92 889 

9.92 881 
9.92 874 
9.92 866 
9.92 858 
9.92 850 

9.92 842 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 






29 


28 


2 


5.8 


5.6 


3 


8.7 


8.4 


4 


11.6 


11.2 


5 


14.5 


14.0 


6 


17.4 


16.8 


7 


20.3 


19.6 


8 


23.2 


22.4 


9 


26.1 


25.2 




21 


20 


2 


4.2 


4.0 


3 


6.3 


6.0 


4 


8.4 


8.0 


5 


10.5 


10.0 


6 


12.6 


12.0 


7 


14.7 


14.0 


8 


16.8 


16.0 


9 


18.9 


18.0 




8 


7 


2 


1.6 


1.4 


3 


2.4 


2.1 


4 


3.2 


2.8 


5 


4.0 


3.5 


6 


4.8 


4.2 


7 


5.6 


4.9 


8 


6.4 


5.6 


9 


7.2 


6.3 



From the top: 

For 31°+ or 211°+ 
read as printed; for 
121 o+ or301 o+ ,read 
co-function. 

From the bottom: 

For58 0+ or238 0+ , 
read as printed ; for 
148 0+ or328 0+ ,read 
co-function. 



LCos d 



LCtn 



cd 



LTan 



LSin 



Prop. Pts. 



58° — Logarithms of Trigonometric Functions 



78 



32° — Logarithms of Trigonometric Functions [III 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.72 421 

9.72 441 
9.72 461 
9.72 482 
9.72 502 

9.72 522 
9.72 542 
9.72 562 
9.72 582 
9.72 602 

9.72 622 
9.72 643 
9.72 663 
9.72 683 
9.72 703 



.72 723 

.72 743 
.72 763 
.72 783 

.72 803 

.72 823 

.72 843 
.72 863 
.72 883 
.72 902 



9.72 922 
9.72 942 
9.72 962 

9.72 982 

9.73 002 

9.73 022 
9.73 041 
9.73 061 
9.73 081 
9.73 101 

9.73 121 
9.73 140 
9.73 160 
9.73 180 
9.73 200 

9.73 219 
9.73 239 
9.73 259 
9.73 278 
9.73 298 

9.73 318 
9.73 337 
9.73 357 
9.73 377 
9.73 396 



.73 416 
.73 435 
.73 455 
.73 474 
.73 494 

.73 513 
.73 533 
.73 552 
.73 572 
.73 591 



9.73 611 



LCos 



d LTan cd L Ctn LCos d 



20 
20 
21 
20 
20 

20 
20 
20 
20 
20 

21 

20 
20 
20 
20 

20 

20 
20 
20 
20 

20 

20 
20 
19 
20 

20 
20 
20 
20 
20 

19 

20 
20 
20 
20 

19 

20 
20 
20 
19 

20 
20 
19 
20 
20 

19 

20 
20 
19 
20 

19 
20 
19 
20 
19 

20 
19 
20 
19 
20 



79 579 
79 607 
79 635 
79 663 
79 691 

79 719 
79 747 
79 776 
79 804 
79 832 

79 860 
79 888 
79 916 
79 944 

79 972 

80 000 
80 028 
80 056 
80 084 
80 112 

80 140 
80 168 
80 195 
80 223 
80 251 

80 279 
80 307 
80 335 
80 363 
80 391 

80 419 
80 447 
80 474 
80 502 
80 530 

80 558 
80 586 
80 614 
80 642 
80 669 

80 697 
80 725 
80 753 
80 781 
80 808 

80 836 
80 864 
80 892 
80 919 
80 947 

80 975 
81003 
81030 
81058 
81086 

81 113 

81 141 
81 169 
.81 196 
.81 224 
,81 252 



LCtn 



28 
28 
28 
28 
28 

28 
29 
28 
28 
28 

28 
28 
28 
28 
28 

28 
28 
28 
28 

28 

28 
27 

28 
28 

28 

28 

28 
28 
28 
28 

28 

27 
28 
28 
28 

28 
28 
28 
27 
28 

28 
28 
28 
27 
28 

28 
28 
27 
28 
28 

28 
27 
28 
28 
27 

28 

28 
27 
28 
28 



10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 
10. 
10. 
10. 
10. 

10. 



20 421 
20 393 
20 365 
20 337 
20 309 

20 281 
20 253 
20 224 
20196 
20168 

20140 
20112 
20 084 
20 056 
20 028 

20 000 
19 972 
19 944 
19 916 

19 888 

19 860 
19 832 
19 805 
19 777 
19 749 
19 721 
19 693 
19 665 
19 637 
19 609 

19 581 
19 553 
19 526 
19 498 
19 470 

19 442 
19 414 
19 386 
19 358 
19 331 

19 303 
19 275 
19 247 
19 219 
19 192 

19 164 
19 136 
19 108 
19 081 
19 053 

19 025 
18 997 
18 970 
18 942' 
18 914 

18 887 
18 859 
18 831 
18 804 
18 776 
18 748 



cd LTan LSin d 



9.92 842 
9.92 834 
9.92 826 
9.92 818 
9.92 810 
9.92 803 
9.92 795 
9.92 787 
9.92 779 
9.92 771 

9.92 763 
9.92 755 
9.92 747 
9.92 739 
9.92 731 
9.92 723 
9.92 715 
9.92 707 
9.92 699 
9.92 691 
9.92 683 
9.92 675 
9.92 667 
9.92 659 
9.92 651 

9.92 643 
9.92 635 
9.92 627 
9.92 619 
9.92 611 

9.92 603 
9.92 595 
9.92 587 
9.92 579 
9.92 571 

9.92 563 
9.92 555 
9.92 546 
9.92 538 
9.92 530 

9.92 522 
9.92 514 
9.92 506 
9.92 498 
9.92 490 
9.92 482 
9.92 473 
9.92 465 
9.92 457 
9.92 449 
9.92 441 
9.92 433 
9.92 425 
9.92 416 
9.92 408 

9.92 400 
9.92 392 
9.92 384 
9.92 376 
9.92 367 

9.92 359 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 

2 
1 





Prop. Pts. 





29 


2 


5.8 


3 


8.7 


4 


11.6 


5 


14.5 


6 


17.4 


7 


20.3 


8 


23.2 


9 


26.1 





27 


2 


5.4 


3 


8.1 


4 


10.8 


5 


13.5 


6 


16.2 


7 


18.9 


8 


21.6 


9 


24.3 



28 

5.6 

8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 

21 

4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
18.9 





20 


19 


2 


4.0 


3.8 


3 


6.0 


5.7 


4 


8.0 


7.6 


5 


10.0 


9.5 


6 


12.0 


11.4 


7 


14.0 


13.3 


8 


16.0 


15.2 


9 


18.0 


17.1 



9 


8 


1.8 


1.6 


2.7 


2.4 


3.6 


3.2 


4.5 


4.0 


5.4 


4.8 


6.3 


5.6 


7.2 


6.4 


8.1 


7.2 



7 

1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 



From the top: 

For32°+or212 0+ , 
read as printed ; for 
122°+or302°\read 

co-function. 

From the bottom: 
For57 0+ or237 0+ , 
read as printed; for 
147°+or327 0+ ,read 
co-function. 



Prop. Pts. 



57° — Logarithms of Trigonometric Functions 



Ill] 33° — Logarithms of Trigonometric Functions 



79 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 

24 

25 

26 

27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

fi 

42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin d LTan cd L Ctn L Cos 



9.73 611 
9.73 630 
9.73 650 
9.73 669 
9.73 689 

9.73 708 
9.73 727 
9.73 747 
9.73 766 
9.73 785 

9.73 805 
9.73 824 
9.73 843 
973 863 
9.73 882 

9.73 901 
9.73 921 
9.73 940 
9.73 959 
9.73 978 

9.73 997 

9.74 017 
9.74 036 
9.74 055 
9.74 074 

9.74 093 
9.74 113 
9.74 132 
9.74 151 
9.74 170 



74 189 
74 208 

74 227 
74 246 
74 265 

,74 284 
,74 303 
.74 322 
.74 341 
.74 360 



9, 
9, 
9, 
9 
9 

9 
9 
9 
9 
9 

9.74 379 
9.74 398 
9.74 417 
9.74 436 
9.74 455 

9.74 474 
9.74 493 
9.74 512 
9.74 531 
9.74 549 



.74 568 
.74 587 
.74 606 
.74 625 
.74 644 

.74 662 
.74 681 
.74 700 
.74 719 
.74 737 



9.74 756 



19 
20 
19 
20 
19 

19 
20 
19 
19 
20 

19 
19 
20 
19 
19 

20 
19 
19 
19 
19 

20 
19 
19 
19 
19 

20 
19 
19 
19 
19 

19 

19 
19 
19 
19 

19 
19 
19 
19 
19 

19 
19 
19 
19 
19 

19 
19 
19 
18 
19 

19 
19 
19 
19 
18 

19 
19 
19 
18 
19 



9.81 252 
9.81 279 
9.81 307 
9.81 335 
9.81 362 

9.81 390 
9.81 418 
9.81 445 
9.81 473 
9.81 500 

9.81 528 
9.81 556 
9.81 583 
9.81611 
9.81 638 

9.81 666 
9.81 693 
9.81 721 
9.81 748 
9.81 776 

9.81 803 
9.81 831 
9.81 858 
9.81 886 
9.81 913 

9.81 941 
9.81 968 

9.81 996 

9.82 023 
9.82 051 

9.82 078 
9.82 106 
9.82 133 
9.82 161 
9.82 188 

9.82 215 
9.82 243 
9.82 270 
9.82 298 
9.82 325 
9.82 352 
9.82 380 
9.82 407 
9.82 435 
9.82 462 

9.82 489 
9.82 517 
9.82 544 
9.82 671 
9.82 599 

9.82 626 
9.82 653 
9.82 681 
9.82 708 
9.82 735 

9.82 762 
9.82 790 
9.82 817 
9.82 844 
9.82 871 

9.82 899 



L Cos d L Ctn 



27 

28 
28 
27 
28 

28 
27 
28 
27 
28 

28 
27 
28 
27 
28 

27 

28 
27 
28 
27 

28 
27 

28 
27 
28 

27 

28 
27 

28 
27 

28 
27 
28 
27 
27 

28 
27 
28 
27 
27 

28 
27 
28 
27 
27 

28 

27 
27 
28 
27 

27 
28 

27 
27 
27 

28 

27 
27 
27 

28 



10.18 748 
10.18 721 
10.18 693 
10.18 665 
10.18 638 

10.18 610 
10.18 582 
10.18 555 
10.18 527 
10.18 500 

10.18472 
10.18 444 
10.18417 
10.18 389 
10.18 362 

10.18 334 
10.18307 
10.18279 
10.18 252 
10.18224 

10.18 197 
10.18169 
10.18 142 
10.18114 
10.18 087 

10.18059 
10.18 032 
10.18 004 
10.17 977 
10.17 949 

10.17 922 
10.17 894 
10.17 867 
10.17 839 
10.17 812 

10.17 785 
10.17 757 
10.17730 
10.17702 
10.17 675 
10.17 648 
10.17 620 
10.17593 
10.17565 
10.17 538 

10.17511 
10.17 483 
10.17456 
10.17429 
10.17401 

10.17 374 
10.17 347 
10.17 319 
10.17292 
10.17265 

10.17238 
10.17 210 
10.17 183 
10.17 156 
10.17 129 

10.17101 



9.92 359 
9.92 351 
9.92 343 
9.92 335 
9.92 326 

9.92 318 
9.92 310 
9.92 302 
9.92 293 
9.92 285 

9.92 277 
9.92 269 
9.92 260 
9.92 252 
9.92 244 

9.92 235 
9.92 227 
9.92 219 
9.92 211 
9.92 202 

9.92 194 
9.92 186 
9.92 177 
9.92 169 
9.92 161 

9.92 152 
9.92 144 
9.92136 
9.92 127 
9.92119 

9.92111 
9.92 102 
9.92 094 
9.92 086 
9.92 077 

9.92 069 
9.92 060 
9.92 052 
9.92 044 
9.92 035 

9.92 027 
9.92 018 
9.92 010 
9.92002 
9.91 993 

9.91 985 
9.91976 
9.91968 
9.91959 
9.91951 

9.91 942 
9.91934 
9.91 925 
9.91917 
9.91908 

9.91 900 
9.91891 
9.91 883 
9.91 874 
9,91 866 

9.91 857 



cd| LTan || LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 





28 


2 


5.6 


3 


8.4 


4 


11.2 


5 


14.0 


6 


16.8 


7 


19.6 


8 


22.4 


9 


25.2 





20 


2 


4.0 


3 


6.0 


4 


8.0 


5 


10.0 


6 


12.0 


7 


14.0 


8 


16.0 


9 


18.0 





IS 


2 


3.6 


3 


5.4 


4 


7.2 


5 


9.0 


6 


10.8 


7 


12.6 


8 


14.4 


9 


16.2 



27 

5.4 
8.1 
10.8 
13.5 
16.2 
18.9 
21.6 
24.3 

19 

3.8 

5.7 

7.6 

9.5 

11.4 

13.3 

15.2 

17.1 

9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 



8 

1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 



From the top: 

For33 0+ or213 0+ , 
read as printed; for 
123 o+ or303 o+ ,read 
co-function. 

From the bottom: 

For56° + or236° + , 

read as printed ; for 
146°+ or 326°+ read 
co-function. 



Prop. Pts. 



56° — Logarithms of Trigonometric Functions 



80 



34° — Logarithms of Trigonometric Functions [in 



o 

i 

2 
3 

4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.74 756 
9.74 775 
9.74 794 
9.74 812 
9.74 831 

9.74 850 
9.74 868 
9.74 887 
9.74 906 
9.74 924 

9.74 943 
9.74 961 
9.74 980 

9.74 999 

9.75 017 

9.75 036 
9.75 054 
9.75 073 
9.75 091 
9.75 110 

9.75 128 
9.75 147 
9.75 165 
9.75 184 
9.75 202 



d J LTan 



75 221 
75 239 
75 258 
75 276 
75 294 

75 313 
75 331 
75 350 
75 368 
75 386 



9, 
9, 
9, 
9. 
9. 

9. 
9. 
9. 
9. 
9. 

9.75 405 
9.75 423 
9.75 441 
9.75 459 
9.75 478 
9.75 496 
9.75 514 
9.75 533 
9.75 551 
9.75 569 

9.75 587 
9.75 605 
9.75 624 
9.75 642 
9.75 660 



.75 678 
.75 696 
.75 714 
.75 733 
.75 751 

.75 769 
.75 787 
.75 805 
.75 823 
.75 841 



9.75 859 



LCos 



19 
19 
18 
19 
19 

18 
19 
19 
18 
19 

18 
19 
19 
18 
19 

18 
19 
18 
19 
18 

19 

18 
19 
18 
19 

18 
19 
18 
18 
19 

18 
19 
18 
18 
19 

18 

18 
18 
19 
18 

18 
19 
18 
18 
18 

18 
19 
18 
18 
18 

18 
18 
19 
18 
18 

18 

18 
18 
18 
18 



9.82 899 
9.82 926 
9.82 953 

9.82 980 

9.83 008 

9.83 035 
9.83 062 
9.83 089 
9.83 117 
9.83 144 

9.83 171 
9.83 198 
9.83 225 
9.83 252 
9.83 280 

9.83 307 
9.83 334 
9.83 361 
9.83 388 
9.83 415 

9.83 442 
9.83 470 
9.83 497 
9.83 524 
9.83 551 

9.83 578 
9.83 605 
9.83 632 
9.83 659 
9.83 686 

9.83 713 
9.83 740 
9.83 768 
9.83 795 
9.83 822 

9.83 849 
9.83 876 
9.83 903 
9.83 930 
9.83 957 

9.83 984 

9.84 011 
9.84 038 
9.84 065 
9.84 092 

9.84 119 
9.84 146 
9.84 173 
9.84 200 
9.84 227 
9.84 254 
9.84 280 
9.84 307 
9.84 334 
9.84 361 

9.84 388 
9.84 415 
9.84 442 
9.84 469 
9.84 496 
9.84 523 



cd 



LCtn 



27 
27 
27 

2S 
27 

27 
27 
28 
27 
27 

27 

27 
27 
28 
27 

27 

27 
27 
27 
27 

28 
27 
27 
27 
27 

27 
27 
27 
27 
27 

27 
28 
27 
27 
27 

27 
27 
27 
27 
27 

27 
27 
27 

27 
27 

27 
27 

27 
27 
27 

26 

27 
27 
27 
27 

27 

27 
27 
27 
27 



LCtn 1 LCos 



cd 



10.17101 
10.17 074 
10.17 047 
10.17 020 
10.16 992 

10.16 965 
10.16 938 
10.16 911 
10.16 883 
10.16 856 

10.16 829 
10.16 802 
10.16 775 
10.16 748 
10.16 720 

10.16 693 
10.16 666 
10.16 639 
10.16 612 
10.16 585 

10.16 558 
10.16 530 
10.16 503 
10.16 476 
10.16 449 

10.16 422 
10.16 395 
10.16 368 
10.16 341 
10.16 314 

10.16 287 
10.16 260 
10.16 232 
10.16 205 
10.16178 

10.16 151 
10.16124 
10.16 097 
10.16 070 
10.16 043 

10.16 016 
10.15 989 
10.15 962 
10.15 935 
10.15 908 

10.15 881 
10.15 854 
10.15 827 
10.15 800 
10.15 773 

10.15 746 
10.15 720 
10.15 693 
10.15 666 
10.15 633 
10.15 612 
10.15 585 
10.15 558 
10.15 531 
10.15 504 

10.15 477 



LTan 



9.91 857 
9.91849 
9.91840 
9.91832 
9.91823 

9.91815 
9.91 806 
9.91798 
9.91 789 
9.91 781 
9.91 772 
9.91 763 
9.91 755 
9.91 746 
9.91 738 

9.91 729 
9.91720 
9.91712 
9.91 703 
9.91 695 

9.91 686 
9.91677 
9.91669 
9.91 660 
9.91651 

9.91 643 
9.91634 
9.91 625 
9.91617 
9.91608 

9.91 599 
9.91591 
9.91582 
9.91573 
9.91565 

9.91556 
9.91547 
9.91538 
9.91530 
9.91521 

9.91512 
9.91504 
9.91495 
9.91486 
9.91477 

9.91469 
9.91460 
9.91451 
9.91442 
9.91433 

9.91425 
9.91416 
9.91407 
9.91398 
9.91389 

9.91 381 
9.91372 
9.91363 
9.91354 
9.91 345 
9.91 336 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 



Prop. Pts. 





28 


2 


5.6 


3 


8.4 


4 


11.2 


5 


14.0 


G 


16.8 


7 


19.6 


8 


22.4 


9 


25.2 





26 


2 


5.2 


3 


7.8 


4 


10.4 


5 


13.0 


6 


15.6 


7 


18.2 


8 


20.8 


9 


23.4 





18 


2 


3.6 


3 


5.4 


4 


7.2 


5 


9.0 


6 


10.8 


7 


12.6 


8 


14.4 


9 


16.2 



27 

5.4 
8.1 
10.8 
13.5 
16.2 
18.9 
21.6 
"24.3 

19 

3.8 

5.7 

7.6 

9.5 

11.4 

13.3 

15.2 

17.1 

9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 



8 

1.6 
2.4 
3.2 
4.0 

4.8 
5.6 
6.4 

7.2 



From the top: 

For34° + or214° + , 
read as printed ; for 
124°+ or 304°+ read 
co-function. 

From the bottom: 

For55° + or235° + , 
read as printed ; for 
145 0+ or325 0+ ,read 
co-function. 



Prop. Pts. 



55° — Logarithms of Trigonometric Functions 



Ill] 35° — Logarithms of Trigonometric Functions 



81 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin 



75 859 
75 877 
75 895 
75 913 
75 931 

75 949 
75 967 

75 985 

76 003 
76 021 

76 039 
76 057 
76 075 
76 093 
76111 

76129 
76146 
76164 
76182 
76 200 

76 218 
76 236 
76 253 
76 271 
76 289 

76 307 
76 324 
76 342 
76 360 
76 378 

76 395 
76 413 
76431 

76 448 
76466 

76484 
76 501 
76 519 
76 537 
76 554 

76 572 
76 590 
76 607 
76 625 
76 642 

76 660 
76 677 
76 695 
76 712 
76 730 

76 747 
76 765 
76 782 
76 800 
76 817 

76 835 

76 852 
76 870 
76 887 
76 904 



LCos 



L Tan cd L Ctn L Cos d 



9.84 523 
9.84 550 
9.84 576 
9.84 603 
9.84 630 

9.84 657 
9.84 684 
9.84 711 
9.84 738 
9.84 764 

9.84 791 
9.84 818 
9.84 845 
9.84 872 
9.84 899 

9.84 925 
9.84 952 

9.84 979 

9.85 006 
9.85 033 

9.85 059 
9.85 086 
9.85113 
9.85 140 
9.85 166 

9.85 193 
9.85 220 
9.85 247 
9.85 273 
9.85 300 

9.85 327 
9.85 354 
9.85 380 
9.85 407 
9.85 434 

9.85 460 
9.85 487 
9,85 514 
9.85 540 
9.85 567 

9.85 594 
9.85 620 
9.85 647 
9.85 674 
9.85 700 

9.85 727 
9.85 754 
9.85 780 
9.85 807 
9.85 834 

9.85 860 
9.85 887 
9.85 913 
9.85 940 
9.85 967 

9.85 993 

9.86 020 
9.86 046 
9.86 073 
9.86 100 
9.86126 



27 
26 
27 
27 
27 

27 
27 
27 
26 
27 

27 
27 
27 
27 
26 

27 
27 
27 
27 
26 

27 
27 
27 
26 
27 

27 
27 
26 
27 

27 

27 
26 

27 
27 
26 

27 
27 
26 
27 
27 
26 
27 
27 
26 
27 

27 
26 
27 
27 
26 

27 
23 
27 
27 
26 

27 

26 
27 
27 
26 



10.15 477 
10.15 450 
10.15 424 
10.15 397 
10.15 370 

10.15 343 
10.15 316 
10.15 289 
10.15 262 
10.15 236 

10.15 209 
10.15182 
10.15 155 
10.15 128 
10.15 101 

10.15 075 
10.15 048 
10.15 021 
10.14 994 
10.14 967 

10.14941 
10.14 914 
10.14 887 
10.14 860 
10.14 834 

10.14 807 
10.14 780 
10.14 753 
10.14 727 
10.14 700 

10.14 673 
10.14 646 
10.14 620 
10.14 593 
10.14 566 

10.14 540 
10.14513 
10.14486 
10.14460 
10.14 433 

10.14 406 
10.14 380 
10.14 353 
10.14 326 
10.14 300 

10.14 273 
10.14 246 
10.14 220 
10.14193 
10.14166 

10.14 140 
10.14113 
10.14 087 
10.14 060 
10.14 033 

10.14 007 
10.13 980 
10.13 954 
10.13 927 
10.13 900 

10.13 874 



L Ctn cd L Tan L Sin d 



9.91336 
9.91328 
9.91319 
9.91310 
9.91301 
9.91292 
9.91283 
9.91274 
9.91266 
9.91257 

9.91 248 
9.91239 
9.91230 
9.91221 
9.91212 

9.91203 
9.91 194 
9.91 185 
9.91 176 
9.91 167 

9.91 158 
9.91 149 
9.91 141 
9.91 132 
9.91 123 

9.91 114 
9.91 105 
9.91096 
9.91087 
9.91078 

9.91 069 
9.91060 
9.91051 
9.91 042 
9.91033 

9.91 023 
9.91014 
9.91 005 
9.90 996 
9.90 987 

9.90 978 
9.90 969 
9.90 960 
9.90 951 
9.90 942 

9.90 933 
9.90 924 
9.90 915 
9.90 906 
9.90 896 

9.90 887 
9.90 878 
9.90 869 
9.90 860 
9.90 851 

9.90 842 
9.90 832 
9.90 823 
9.90 814 
9.90 805 

9.90 796 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 



Prop. Pts. 





27 


2 


5.4 


3 


8.1 


4 


10.8 


5 


13.5 


6 


16.2 


7 


18.9 


8 


21.6 


9 


24.3 





18 


2 


3.6 


3 


5.4 


4 


7.2 


5 


9.0 


6 


10.8 


7 


12.6 


8 


14.4 


9 


16.2 





10 


2 


2.0 


3 


3.0 


4 


4.0 


5 


5.0 


6 


6.0 


7 


7.0 


8 


8.0 


9 


9.0 



26 
5.2 

7.8 
10.4 
13.0 
15.6 

18.2 
20.8 
23.4 

17 

3.4 
5.1 

6.8 
8.5 
10.2 
11.9 
13.6 
15.3 

9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 



8 

1.6 
2.4 
3.2 
4.0 

4.8 
5.6 
6.4 

7.2 



From the top: 

For35 0+ or215 0+ , 
read as printed; for 
125°+ or 305°+ read 
co-function. 

From the bottom: 

For 54°+ or 234°+ 
read as printed ; for 
144°+ or 324°+ read 
co-function. 



Prop. Pts. 



54° — Logarithms of Trigonometric Functions 



82 



36° — Logarithms of Trigonometric Functions [III 



o 

i 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin 



9.76 922 
9.76 939 
9.76 957 
9.76 974 

9.76 991 

9.77 009 
9.77 026 
9.77043 
9.77 061 
9.77078 

9.77 095 
9.77112 
9.77 130 
9.77 147 
9.77 164 

9.77 181 
9.77 199 
9.77216 
9.77233 
9.77 250 

9.77268 
9.77 285 
9.77302 
9.77319 
9.77336 

9.77353 
9.77 370 
9.77387 
9.77405 
9.77422 

9.77439 
9.77456 
9.77473 
9.77490 
9.77507 



77524 
77 541 
77 558 
77575 
77 592 

77 609 
77 626 
77 643 
77 660 
77 677 



9.77 694 
9.77711 
9.77728 
9.77744 
9.77761 



77 778 
77 795 
77 812 
77 829 
77 846 

77862 
77 879 
77 896 
77 913 
77930 

77946 



LCos 



17 
18 
17 
17 
18 

17 

17 
18 
17 
17 

17 
18 
17 
17 
17 

18 
17 
17 
17 
18 

17 
17 
17 
17 
17 

17 
17 
18 
17 
17 

17 

17 
17 
17 
17 

17 
17 
17 
17 
17 

17 
17 
17 
17 
17 

17 
17 
16 
17 
17 

17 
17 
17 
17 

16 

17 
17 
17 
17 
16 



L Tan cd 



9.86 126 
9.86 153 
9.86 179 
9.86 206 
9.86 232 

9.86 259 
9.86 285 
9.86 312 
9.86 338 
9.86365 
9.86392 
9.86418 
9.86445 
9.86471 
9.86498 

9.86524 
9.86 551 
9.86577 
9.86 603 
9.86 630 

9.86656 
9.86 683 
9.86709 
9.86736 
9.86762 

9.86789 
9.86 815 
9.86842 
9.86868 
9.86 894 

9.86921 

9.86 947 
9.86974 

9.87 000 
9.87027 

9.87053 
9.87079 
9.87 106 
9.87 132 
9.87 158 
9.87 185 
9.87 211 
9.87238 
9.87264 
9.87 290 

9.87 317 
9.87343 
9.87369 
9.87 396 
9.87422 

9.87448 
9.87475 
9.87501 
9.87 527 
9.87554 

9.87580 
9.87606 
9.87 633 
9.87 659 
9.87 685 
9.87 711 



d L Ctn cd 



27 
26 
27 
26 
27 

26 
27 
26 
27 
27 

26 
27 
26 
27 
26 

27 
26 
26 
27 
26 

27 
26 
27 
26 
27 
26 
27 
26 
26 
27 

26 
27 
26 
27 
26 

26 

27 
26 
26 
27 

26 
27 
26 
26 
27 

26 
26 
27 
26 
26 

27 
26 
26 
27 
26 

26 
27 
26 
26 
26 



L Ctn L Cos 



0.13 874 
0.13 847 
0.13 821 
0.13 794 
0.13 768 

0.13 741 
0.13 715 
0.13 688 
0.13 662 
0.13 635 

0.13 608 
0.13 582 
0.13 555 
0.13 529 
0.13 502 

0.13 476 
0.13 449 
0.13423 
0.13 397 
0.13 370 

0.13 344 
0.13 317 
0.13 291 
0.13 264 
0.13 238 

0.13 211 
0.13 185 
0.13 158 
0.13 132 
0.13 106 

0.13 079 
0.13 053 
0.13 026 
0.13 000 
0.12 973 

0.12 947 
0.12 921 
0.12 894 
0.12 868 
0.12 842 

0.12 815 
0.12 789 
0.12 762 
0.12 736 
0.12 710 

0.12 683 
0.12 657 
0.12 631 
0.12 604 
0.12 578 
0.12 552 
0.12 525 
0.12499 
0.12 473 
0.12446 

0.12 420 
0.12 394 
0.12 367 
0.12 341 
0.12 315 

10.12 289 



LTan LSin 



9.90 796 
9.90 787 
9.90777 
9.90768 
9.90 759 

9.90 750 
9.90 741 
9.90 731 
9.90 722 
9.90 713 

9.90704 
9.90694 
9.90685 
9.90 676 
9.90 667 

9.90 657 
9.90648 
9.90 639 
9.90630 
9.90620 

9.90611 
9.90 602 
9.90592 
9.90583 
9.90574 

9.90565 
9.90555 
9.90546 
9.90537 
9.90527 

9.90 518 
9.90 509 
9.90499 
9.90490 
9.90480 

9.90471 
9.90462 
9.90452 
9.90443 
9.90434 

9.90424 
9.90415 
9.90405 
9.90 396 
9.90386 

9.90 377 
9.90 368 
9.90 358 
9.90 349 
9.90 339 

9.90 330 
9.90 320 
9.90 311 
9.90 301 
9.90292 

9.90282 
9.90 273 
9.90 263 
9.90 254 
9.90 244 

9.90 235 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 
14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 





27 


2 


5.4 


3 


8.1 


4 


10.8 


5 


13.5 


6 


16.2 


7 


18.9 


8 


21.6 


9 


24.3 



26 

5.2 

7.8 
10.4 
13.0 
15.6 
18.2 
20.8 
23.4 





18 


17 


2 


3.6 


3.4 


3 


5.4 


5.1 


4 


7.2 


6.8 


5 


9.0 


8.5 


6 


10.8 


10.2 


7 


12.6 


11.9 


8 


14.4 


13.6 


9 


16.2 


15.3 




16 


10 


2 


3.2 


2.0 


3 


4.8 


3.0 


4 


6.4 


4.0 


5 


8.0 


5.0 


6 


9.6 


6.0 


7 


11.2 


7.0 


8 


12.8 


8.0 


9 


14.4 


9.0 




9 


2 


1.8 


3 


2.7 


4 


3.6 


5 


4.5 


6 


5.4 


7 


6.3 


8 


7.2 


9 


8.1 


From the top: 


For36 0+ or216 0+ , 


read as printed ; for 


126 o+ or306 o+ ,read 


co-function. 


From the bottom: 


For 53°+ or 233°+ 


read as printed ; for 


143 0+ or323 0+ ,read 


co-functi 


on 


• 



Prop. Pts. 



53° — Logarithms of Trigonometric Functions 



Ill] 37° — Logarithms of Trigonometric Functions 



83 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 
55 
56 
57 
58 
59 

60 



LSin 



9.77 946 
9.77 963 

9.77 980 
9.77997 

9.78 013 

9.78 030 
9.78 047 
9.78 063 
9.78 080 
9.78 097 

9.78113 
9.78 130 
9.78 147 
9.78 163 
9.78 180 



.78 197 
.78 213 
.78230 
.78246 
.78 263 

.78280 
.78 296 
.78 313 
.78 329 
.78346 



9.78 362 
9.78 379 
9.78395 
9.78412 
9.78428 

9.78445 
9.78 461 

9.78478 
9.78494 
9.78 510 

9.78 527 
9.78 543 
9.78 560 
9.78576 
9.78 592 

9.78 609 
9.78 625 
9.78 642 
9.78 658 
9.78 674 

9.78 691 
9.78 707 
9.78723 
9.78739 
9.78756 



.78772 
.78 788 
.78 805 
.78 821 
.78 837 

.78 853 
.78869 
.78886 
.78902 
.78918 

.78934 



LCos 



17 
17 
17 
16 
17 

17 

16 
17 
17 
16 

17 

17 
16 
17 
17 
16 
17 
16 
17 
17 
16 
17 
16 
17 
16 

17 
16 
17 
16 
17 

16 
17 
16 
16 
17 

16 
17 
16 
16 
17 

16 
17 
16 
16 
17 

16 
16 
16 
17 
16 

16 
17 
16 
16 
16 

16 
17 
16 
16 
16 



LTan 



9.87 711 

9.87 738 
9.87 764 
9.87 790 
9.87817 

9.87 843 
9.87 869 
9.87 895 

9.87 922 
9.87948 

9.87974 
9.88000 

9.88 027 
9.88 053 
9.88079 

9.88 105 
9.88131 
9.88 158 
9.88 184 
9.88 210 

9.88236 
9.88 262 
9.88289 
9.88 315 
9.88341 

9.88 367 
9.88 393 
9.88420 
9.88446 
9.88472 

9.88498 
9.88 524 
9.88550 
9.88 577 
9.88 603 

9.88 629 
9.88 655 
9.88 681 
9.88707 
9.88733 
9.88 759 
9.88786 
9.88 812 
9.88 838 
9.88 864 

9.88 890 
9.88 916 
9.88 942 
9.88 968 

9.88 994 

9.89 020 
9.89 046 
9.89 073 
9.89 099 
9.89 125 

9.89 151 
9.89 177 
9.89 203 
9.89 229 
9.89 255 

9.89 281 



cd 



L Ctn cd 



27 
26 
26 
27 
26 

26 
26 
27 
26 
26 
26 
27 
26 
26 
26 

26 
27 
26 
26 
26 
26 
27 
26 
26 
26 

26 
27 
26 
26 
26 

26 
26 
27 
26 
26 

26 
26 
26 
26 
26 

27 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
27 
26 
26 
26 

26 
26 
26 
26 
26 



LCtn 



10.12 289 
10.12 262 
10.12 236 
10.12 210 
10.12 183 

10.12 157 
10.12131 
10.12105 
10.12 078 
10.12 052 

10.12 026 
10.12 000 
10.11973 
10.11947 
10.11921 

10.11895 
10.11869 
10.11842 
10.11816 
10.11790 

10.11764 
10.11738 
10.11711 
10.11685 
10.11659 
10.11 633 
10.11607 
10.11580 
10.11554 
10.11528 

10.11502 
10.11476 
10.11450 
10.11423 
10.11397 
10.11371 
10.11345 
10.11319 
10.11293 
10.11267 

10.11241 
10.11214 
10.11 188 
10.11 162 
10.11 136 

10.11 110 
10.11084 
10.11058 
10.11032 
10.11006 

10.10980 
10.10 954 
10.10 927 
10.10 901 
10.10875 

10.10 849 
10.10 823 
10.10797 
10.10771 
10.10 745 
10.10 719 



LCos 



LTan 



9.90 235 
9.90 225 
9.90 216 
9.90 206 
9.90 197 

9.90 187 
9.90 178 
9.90 168 
9.90 159 
9.90 149 

9.90 139 
9.90 130 
9.90 120 
9.90111 
9.90 101 

9.90091 
9.90 082 
9.90 072 
9.90 063 
9.90 053 

9.90 043 
9.90 034 
9.90 024 
9.90 014 
9.90005 

9.89 995 
9.89 985 
9.89 976 
9.89 966 
9.89 956 

9.89 947 
9.89 937 
9.89 927 
9.89 918 
9.89 908 

9.89 898 
9.89 888 
9.89 879 
9.89 869 
9.89 859 

9.89 849 
9.89 840 
9.89 830 
9.89 820 
9.89 810 

9.89 801 
9.89 791 
9.89 781 
9.89 771 
9.89 761 

9.89 752 
9.89 742 
9.89 732 
9.89 722 
9.89 712 

9.89 702 
9.89 693 
9.89 683 
9.89 673 
9.89 663 

9.89 653 



LSin 



10 
9 

10 
9 

10 

9 
10 

9 

10 
10 

9 
10 

9 
10 
10 

9 
10 

9 

10 
10 

9 

10 

10 

9 

10 

10 

9 

10 

10 

9 

10 
10 
9 
10 
10 

10 
9 
10 
10 
10 

9 

10 

10 

10 

9 

10 
10 
10 
10 
9 

10 
10 
10 
10 
10 

9 

10 
10 

10 
10 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop, Pts. 





27 


26 


2 


5.4 


5.2 


3 


8.1 


7.8 


4 


10.8 


10.4 


5 


13.5 


13.0 


6 


16.2 


15.6 


7 


18.9 


18.2 


8 


21.6 


20.8 


9 


24.3 


23.4 




17 


16 


2 


3.4 


3.2 


3 


5.1 


4.8 


4 


6.8 


6.4 


5 


8.5 


8.0 


6 


10.2 


9.6 


7 


11.9 


11.2 


8 


13.6 


12.8 


9 


15.3 


14.4 





10 


2 


2.0 


3 


3.0 


4 


4.0 


5 


5.0 


6 


6.0 


7 


7.0 


8 


8.0 


9 


9.0 



9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 



From the top: 

For 37°+ or 217°+ 
read as printed ; for 
127°+or307 o+ ,read 
co-function. 

From the bottom: 

For52 0+ or232 0+ , 
read as printed; for 
142°+ or 322°+ read 
co-function. 



Prop. Pts. 



52° — Logarithms of Trigonometric Functions 



84 



38° — Logarithms of Trigonometric Functions [III 



o 

i 

2 

3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 

38 
39 

40 

41 

42 
43 

44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 



LSin 



9.78 934 
9.78 950 
9.78 967 
9.78 983 

9.78 999 

9.79 015 
9.79 031 
9.79 047 
9.79 063 
9.79 079 

9.79 095 
9.79111 
9.79 128 
9.79 144 
9.79 160 
9.79 176 
9.79 192 
9.79 208 
9.79 224 
9.79 240 

9.79 256 
9.79 272 
9.79 288 
9.79 304 
9.79 319 

9.79 335 
9.79 351 
9.79 367 
9.79 383 
9.79 399 

9.79 415 
9.79 431 
9.79 447 
9.79 463 
9.79478 
9.79 494 
9.79 510 
9.79 526 
9.79 542 
9.79 558 

9.79 573 
9.79 589 
9.79 605 
9.79 621 
9.79 636 

9.79 652 
9.79 668 
9.79 684 
9.79 699 
9.79 715 



79 731 
79 746 
79 762 
79 778 
79 793 

79 809 
79 825 
79 840 
79 856 
79 872 



9.79 887 



LCos 



16 
17 

16 
16 
16 

16 
16 
16 
16 
16 

16 
17 
16 
16 
16 

16 
16 
16 
16 
16 

16 
16 
16 
15 
16 

16 
16 
16 
16 
16 

16 
16 
16 
15 
16 

16 
16 
16 
16 
15 

16 
16 
16 
15 
16 

16 
16 
15 
16 
16 

15 
16 
16 
15 
16 

16 
15 
16 
16 
15 



L Tan cd 



89 281 
89 307 
89 333 
89 359 
89 385 

89 411 
89 437 
89 463 
89 489 
89 515 
89 541 
89 567 
89 593 
89 619 
89 645 

89 671 

89 697 
89 723 
89 749 
89 775 

89 801 
89 827 
89 853 
89 879 
89 905 

89 931 
89 957 

89 983 

90 009 
90 035 

90 061 
90 086 
90112 
90138 
90164 

90190 
90 216 
90 242 
90 268 
90 294 

90 320 
90 346 
90 371 
90 397 
90423 
90449 
90475 
90 501 
90 527 
90 553 

90 578 
90 604 
90 630 
90 656 
90 682 

90 708 
90 734 
.90 759 
.90 785 
.90 811 

90 837 



26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
26 
26 
26 
26 

25 
26 
26 
26 
26 

26 
26 
26 
26 
26 

26 
25 
26 
26 
26 

26 
26 
26 
26 
25 
26 
26 
26 
26 
26 

26 
25 
26 
26 
26 



LCtn 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 
4 
3 
2 
1 
J) 
d LCtn cdl L Tan I LSin d ' 



10.10 719 
10.10 693 
10.10 667 
10.10 641 
10.10 615 

10.10 589 
10.10 563 
10.10 537 
10.10511 
10.10485 

10.10459 
10.10433 
10.10 407 
10.10 381 
10.10 355 

10.10 329 
10.10 303 
10.10 277 
10.10 251 
10.10225 

10.10199 
10.10173 
10.10147 
10.10121 
10.10 095 

10.10 069 
10.10 043 
10.10 017 
10.09 991 
10.09 965 

10.09 939 
10.09 914 
10.09 888 
10.09 862 
10.09 836 

10.09 810 
10.09 784 
10.09 758 
10.09 732 
10.09 706 

10.09 680 
10.09 654 
10.09 629 
10.09 603 
10.09 577 
10.09 551 
10.09 525 
10.09 499 
10.09 473 
10.09 447 
10.09 422 
10.09 396 
10.09 370 
10.09 344 
10.09 318 

10.09 292 
10.09 266 
10.09 241 
10.09 215 
10.09 189 
10.09 163 



LCos d 



9.89 653 
9.89 643 
9.89 633 
9.89 624 
9.89 614 

9.89 604 
9.89 594 
9.89 584 
9.89 574 
9.89 564 
9.89 554 
9.89 544 
9.89 534 
9.89 524 
9.89 514 

9.89 504 
9.89 495 
9.89 485 
9.89475 
9.89 465 

9.89 455 
9.89 445 
9.89 435 
9.89 425 
9.89 415 

9.89 405 
9.89 395 
9.89 385 
9.89 375 
9.89 364 

9.89 354 
9.89 344 
9.89 334 
9.89 324 
9.89 314 

9.89 304 
9.89 294 
9.89 284 
9.89 274 
9.89 264 

9.89 254 
9.89 244 
9.89 233 
9.89 223 
9.89 213 

9.89 203 
9.89 193 
9.89 183 
9.89 173 
9.89 162 

9.89 152 
9.89 142 
9.89 132 
9.89 122 
9.89 112 

9.89 101 
9.89 091 
9.89 081 
9.89 071 
9.89 060 

9.89 050 



Prop. Pts. 





26 


2 


5.2 


3 


7.8 


4 


10.4 


5 


13.0 


6 


15.6 


7 


18.2 


8 


20.8 


9 


23.4 





17 


2 


3.4 


3 


5.1 


4 


6.8 


5 


8.5 


6 


10.2 


7 


11.9 


8 


13.6 


9 


15.3 



25 

5.0 
7.5 

10.0 
12.5 
15.0 
17.5 
20.0 
22.5 

16 

3.2 

4.8 

6.4 

8.0 

9.6 

11.2 

12.8 

14.4 

11 

2.2 
3.3 

4.4 
5.5 
6.6 

7.7 
8.8 
9.9 

9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 



From the top: 

For38° + or218°+ 
read as printed ; for 
128 o+ or308 o+ ,read 

co-function. 

From the bottom: 
For51° + or231°+ 
read as printed ; for 
141° + or321° + ,read 
co-function. 





15 


2 


3.0 


3 


4.5 


4 


6.0 


5 


7.5 


6 


9.0 


7 


10.5 


8 


12.0 


9 


13.5 





10 


2 


2.0 


3 


3.0 


4 


4.0 


5 


5.0 


6 


6.0 


7 


7.0 


8 


8.0 


9 


9.0 



Prop. Pts. 



51° — Logarithms of Trigonometric Functions 



[Ill 39° — Logarithms of Trigonometric Functions 



85 



r 





1 

2 

3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 

54 

55 

56 
57 

58 
59 

60 



LSin 



.79 887 
.79 903 
.79 918 
.79 934 
.79 950 

.79 965 
.79 981 
.79 996 
.80 012 
.80 027 

.80 043 
.80 058 
.80 074 
.80 089 
.80 105 

.80 120 
.80 136 
.80151 
.80 166 
.80 182 

.80 197 
.80 213 
.80 228 
.80 244 
.80 259 

.80 274 
.80 290 
.80 305 
.80 320 
.80 336 

,80 351 
,80 366 

,80 382 
,80 397 
,80412 

,80428 
.80 443 
,80 458 
,80 473 
.80 489 

,80 504 
,80 519 
,80 534 
,80 550 
,80 565 

,80 580 
,80 595 
80 610 
80 625 
80 641 

,80 656 
80 671 
80 686 
80 701 
80 716 

80 731 
80 746 
80 762 
80 777 
80 792 

80 807 



LCos 



LTan 



9.90 837 
9.90 863 
9.90 889 
9.90 914 
9.90 940 

9.90 966 

9.90 992 
9.91018 
9.91043 

9.91 069 

9.91095 
9.91 121 
9.91 147 
9.91 172 
9.91 198 

9.91 224 
9.91250 
9.91276 
9.91301 
9.91327 

9.91 353 
9.91379 
9.91404 
9.91430 
9.91456 
9.91482 
9.91507 
9.91533 
9.91559 
9.91585 

9.91610 
9.91636 
9.91 662 
9.91 688 
9.91713 

9.91 739 
9.91765 
9.91791 
9.91816 
9.91 842 

9.91 868 

9.91 893 
9.91919 
9.91945 
9.91971 

9.91996 

9.92 022 
9.92 048 
9.92 073 
9.92 099 

9.92 125 
9.92 150 
9.92 176 
9.92 202 
9.92 227 

9.92 253 
9.92 279 
9.92 304 
9.92 330 
9.92 356 
9.92 381 



L Ctn 



cd L Ctn L Cos 



26 
26 
25 
26 
26 

26 
26 
25 
26 
26 

26 
26 
25 
26 
26 

26 

26 
25 
26 
26 

26 
25 
26 
26 
26 

25 

26 
26 
26 
25 

26 
26 
26 
25 
26 

26 
26 
25 
26 
26 

25 

26 
26 
26 
25 

26 
26 
25 
26 
26 

25 
26 
26 
25 
26 

26 
25 

26 
26 
25 



cd 



10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 
10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 

10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10 

10 
10 
10 
10 
10, 
10, 



,09 163 
09 137 
09 111 
09 086 
09 060 

,09 034 

09 008 
08 982 
08 957 
08 931 

08 905 
08 879 
08 853 
08 828 
08 802 

08 776 
08 750 
08 724 
08 699 
08 673 

08 647 
08 621 
08 596 
08 570 
08 544 

08 518 
,08 493 
.08 467 
.08 441 
.08 415 

.08 390 
.08 364 
.08 338 
.08312 
.08 287 

.08 261 
.08 235 
.08 209 
.08 184 
.08 158 
.08 132 
.08 107 
.08 081 
.08 055 
.08 029 

.08 004 
.07 978 
.07 952 
.07 927 
.07 901 
.07 875 
.07 850 
.07 824 
.07 798 
.07 773 

.07 747 
.07 721 
.07 696 
.07 670 
,07 644 

,07 619 



LTan 



9.89 050 
9.89 040 
9.89 030 
9.89 020 
9.89 009 

9.88 999 
9.88 989 
9.88 978 
9.88 968 
9.88 958 
9.88 948 
9.88 937 
9.88 927 
9.88 917 
9.88 906 

9.88 896 
9.88 886 
9.88 875 
9.88 865 
9.88 855 

9.88 844 
9.88 834 
9.88 824 
9.88 813 
9.88 803 

9.88 793 
9.88 782 
9.88 772 
9.88 761 
9.88 751 
9.88 741 
9.88 730 
9.88 720 
9.88 709 
9.88 699 

9.88 688 
9.88 678 
9.88 668 
9.88 657 
9.88 647 

9.88 636 
9.88 626 
9.88 615 
9.88 605 
9.88 594 

9.88 584 
9.88 573 
9.88 563 
9.88 552 
9.88 542 

9.88 531 
9.88 521 
9.88 510 
9.88 499 
9.88 489 

9.88 478 
9.88 468 
9.88 457 
9.88 447 
9.88 436 
9.88 425 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 





26 


25 


2 


5.2 


5.0 


3 


7.8 


7.5 


4 


10.4 


10.0 


5 


13.0 


12.5 


6 


15.6 


15.0 


7 


18.2 


17.5 


8 


20.8 


20.0 


9 


23.4 


22.5 




16 


13 


2 


3.2 


3.0 


3 


4.8 


4.5 


4 


6.4 


6.0 


5 


8.0 


7.5 


6 


9.6 


9.0 


7 


11.2 


10.5 


8 


12.8 


12.0 


9 


14.4 


13.5 




11 


10 


2 


2.2 


2.0 


3 


3.3 


3.0 


4 


4.4 


4.0 


5 


5.5 


5.0 


6 


6.6 


6.0 


7 


7.7 


7.0 


8 


8.8 


8.0 


9 


9.9 


9.0 



From the top: 

For39°+or219° + , 

read as printed ; for 
129 o+ or309 o+ ,read 

co-function . 

From the bottom: 

For50 o+ or230 o+ , 

read as printed ; for 
140°+ or 320°+ read 
co-function. 



Prop. Pts. 



50° — Logarithms of Trigonometric Functions 



86 



40° — Logarithms of Trigonometric Functions [III 





l 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 

47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 



LSin 



9.80 807 
9.80 822 
9.80 837 
9.80 852 
9.80 867 
9.80 882 
9.80 897 
9.80 912 
9.80 927 
9.80 942 

9.80 957 
9.80 972 

9.80 987 

9.81 002 
9.81017 

9.81 032 
9.81 047 
9.81061 
9.81076 
9.81091 

9.81 106 
9.81 121 
9.81 136 
9.81 151 
9.81 166 

9.81 180 
9.81 195 
9.81210 
9.81 225 
9.81 240 

9.81 254 
9.81 269 
9.81 284 
9.81 299 
9.81314 

9.81 328 
9.81 343 
9.81358 
9.81 372 
9.81 387 

9.81 402 
9.81417 
9.81431 
9.81 446 
9.81461 



.81 475 
.81 490 
.81 505 
.81519 
.81 534 

.81 549 
.81 563 
.81 578 
.81 592 
.81 607 



9.81 622 
9.81 636 
9.81651 
9.81 665 
9.81 680 

9.81 694 



LCos 



L Tan cd 



9.92 
9.92 
9.92 
9.92 
9.92 

9.92 
9.92 
9.92 
9.92 
9.92 

9.92 
9.92 
9.92 
9.92 
9.92 

9.92 
9.92 
9.92 
9.92 
9.92 

9.92 
9.92 
9.92 
9.92 
9.92 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 
9.93 
9.93 
9.93 
9.93 

9.93 



381 
407 
433 

458 
484 

510 
535 
561 

587 
612 

638 
663 
689 
715 
740 

766 

792 
817 
843 
868 

894 
920 
945 
971 
996 

022 
048 
073 
099 
124 

150 
175 
201 
227 
252 

278 
303 
329 
354 
380 

406 
431 
457 

482 
508 

533 
559 

584 
610 
636 

661 
687 
712 
738 
763 

789 
814 
840 
865 
891 

916 



d L Ctn cd 



26 
26 
25 
26 
26 

25 
26 
26 
25 
26 

25 
26 
26 
25 
26 

26 
25 
26 
25 
26 

26 
25 
26 
25 
26 

26 
25 
26 
25 
26 

25 
26 
26 
25 
26 

25 
26 
25 
26 
26 

25 
26 
25 
26 
25 

26 
25 
26 
26 
25 

26 
25 
26 
25 
26 

25 

26 
25 
26 
25 



L Ctn L Cos 



0.07 619 
0.07593 
0.07 567 
0.07 542 
0.07 516 

0.07490 
0.07 465 
0.07 439 
0.07413 
0.07 388 

0.07362 
0.07 337 
0.07 311 
0.07 285 
0.07260 

0.07 234 
0.07 208 
0.07 183 
0.07 157 
0.07 132 

0.07 106 
0.07 080 
0.07 055 
0.07 029 
0.07 004 

0.06 978 
0.06 952 
0.06 927 
0.06 901 
0.06 876 

0.06 850 
0.06 825 
0.06 799 
0.06 773 
0.06 748 
0.06 722 
0.06 697 
0.06 671 
0.06 646 
0.06 620 

0.06 594 
0.06 569 
0.06 543 
0.06 518 
0.06492 

0.06467 
0.06441 
0.06416 
0.06 390 
0.06 364 

0.06 339 
0.06 313 
0.06 288 
0.06 262' 
0.06 237 
0.06 211 
0.06 186 
0.06 160 
0.06 135 
0.06 109 
10.06 084 



9.88425 
9.88 415 
9.88404 
9.88 394 
9.88 383 

9.88 372 
9.88 362 
9.88 351 
9.88 340 
9.88 330 

9.88319 
9.88 308 
9.88 298 
9.88 287 
9.88 276 

9.88 266 
9.88 255 
9.88244 
9.88 234 
9.88 223 

9.88 212 
9.88 201 
9.88 191 
9.88 180 
9.88 169 

9.88 158 
9.88 148 
9.88 137 
9.88 126 
9.88115 

9.88 105 
9.88 094 
9.88 083 
9.88 072 
9.88 061 

9.88 051 
9.88 040 
9.88 029 
9.88 018 
9.88 007 

9.87 996 
9.87 985 
9.87975 
9.87964 
9.87 953 

9.87 942 
9.87 931 
9.87 920 
9.87 909 
9.87 898 

9.87 887 
9.87 877 
9.87866 
9.87 855 
9.87 844 

9.87 833 

9.87 822 
9.87 811 
9.87 800 
9.87 789 

9.87 778 



L Tan L Sin d 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 





26 


25 


2 


5.2 


5.0 


3 


7.8 


7.5 


4 


10.4 


10.0 


5 


13.0 


12.5 


6 


15.6 


15.0 


7 


18.2 


17.5 


8 


20.8 


20.0 


9 


23.4 


22.5 




15 


14 


2 


3.0 


2.8 


3 


4.5 


4.2 


4 


6.0 


5.6 


5 


7.5 


7.0 


6 


9.0 


8.4 


7 


10.5 


9.8 


8 


12.0 


11.2 


9 


13.5 


12.6 




11 


10 


2 


2.2 


2.0 


3 


3.3 


3.0 


4 


4.4 


4.0 


5 


5.5 


5.0 


6 


6.6 


6.0 


7 


7.7 


7.0 


8 


8.8 


8.0 


9 


9.9 


9.0 



From the top: 

For40 o+ or220 o+ , 

read as printed; for 
130 o+ or310 o+ ,read 

co-function. 

From the bottom: 

For49 0+ or229 0+ , 
read as printed ; for 
139° + or319° + ,read 
co-function. 



Prop. Pts. 



49° — Logarithms of Trigonometric Functions 



Ill] 41° — Logarithms of Trigonometric Functions 



87 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.81 694 
9.81 709 
9.81 723 
9.81 738 
9.81 752 

9.81 767 
9.81781 
9.81 796 
9.81810 
9.81 825 

9.81 839 
9.81 854 
9.81 868 
9.81 882 
9.81 897 

9.81911 
9.81 926 
9.81 940 
9.81 955 
9.81 969 

9.81 983 

9.81 998 

9.82 012 
9.82 026 
9.82 041 

9.82 055 
9.82 069 
9.82 084 
9.82 098 
9.82112 



.82 126 
.82 141 
.82 155 
.82 169 
.82 184 

.82 198 
.82 212 
.82 226 
.82 240 
.82 255 



9.82 269 
9.82 283 
9.82 297 
9.82 311 
9.82 326 

9.82 340 
9.82 354 
9.82 368 
9.82 382 
9.82 396 



.82 410 
.82 424 
.82439 
.82 453 

.82 467 
.82 481 
.82495 
.82 509 
.82 523 
.82 537 

.82 551 



LCos 



15 
14 
15 
14 
15 

14 

15 
14 
15 
14 

15 
14 
14 
15 
14 

15 
14 
15 
14 
14 

15 
14 
14 
15 
14 

14 
15 
14 
14 
14 

15 
14 
14 
15 
14 

14 
14 
14 
15 
14 

14 
14 
14 
15 
14 

14 
14 
14 
14 
14 

14 
15 
14 
14 
14 

14 
14 
14 
14 
14 



LTan 



9.93 916 
9.93 942 
9.93 967 

9.93 993 

9.94 018 

9.94 044 
9.94 069 
9.94 095 
9.94 120 
9.94 146 

9.94 171 
9.94 197 
9.94 222 
9.94 248 
9.94 273 

9.94 299 
9.94 324 
9.94 350 
9.94 375 
9.94401 

9.94426 
9.94452 
9.94477 
9.94 503 
9.94 528 

9.94 554 
9.94 579 
9.94 604 
9.94 630 
9.94 655 

9.94 681 
9.94 706 
9.94 732 
9.94 757 
9.94 783 

9.94 808 
9.94 834 
9.94 859 
9.94 884 
9.94 910 

9.94 935 
9.94 961 

9.94 986 

9.95 012 
9.95 037 

9.95 062 
9.95 088 
9.95113 
9.95 139 
9.95 164 

9.95 190 
9.95 215 
9.95 240 
9.95 266 
9.95 291 

9.95 317 
9.95 342 
9.95 368 
9.95 393 
9.95 418 
9.95 444 



cd 



26 
25 
26 
25 
26 

25 
26 
25 
26 
25 

26 
25 
26 
25 
26 

25 
26 
25 
26 
25 

26 
25 
26 
25 
26 

25 
25 
26 
25 
26 

25 
26 
25 
26 
25 

26 
25 
25 
26 
25 

26 
25 
26 
25 
25 

26 
25 
26 
25 
26 

25 

25 
26 
25 
26 

25 

26 
25 
25 
26 



d L Ctn cd 



LCtn 



0.06 084 
0.06 058 
0.06 033 
0.06 007 
0.05 982 

0.05 956 
0.05 931 
0.05 905 
0.05 880 
0.05 854 

0.05 829 
0.05 803 
0.05 778 
0.05 752 
0.05 727 

0.05 701 
0.05 676 
0.05 650 
0.05 625 
0.05599 

0.05 574 
0.05 548 
0.05 523 
0.05 497 
0.05 472 

0.05 446 
0.05421 
0.05 396 
0.05 370 
0.05 345 

0.05 319 
0.05 294 
0.05 268 
0.05 243 
0.05 217 
0.05 192 
0.05 166 
0.05 141 
0.05116 
0.05 090 

0.05 065 
0.05 039 
0.05 014 
0.04 988 
0.04 963 

0.04 938 
0.04 912 
0.04 887 
0.04 861 
0.04 836 

0.04 810 
0.04 785 
0.04 760 
0.04 734 
0.04 709 

0.04 683 
0.04 658 
0.04 632 
0.04 607 
0.04 582 

10.04 556 



LTan 



LCos 



9.87 778 
9.87 767 
9.87 756 
9.87 745 
9.87734 

9.87 723 
9.87 712 
9.87701 
9.87 690 
9.87 679 

9.87 668 
9.87 657 
9.87 646 
9.87 635 
9.87 624 

9.87 613 
9.87 601 
9.87590 
9.87579 

9.87 568 

9.87 557 
9.87 546 
9.87535 
9.87 524 
9.87513 

9.87501 
9.87490 
9.87479 
9.87468 
9.87 457 

9.87446 
9.87434 
9.87423 
9.87412 
9.87401 

9.87 390 
9.87 378 
9.87 367 
9.87 356 
9.87 345 

9.87 334 
9.87 322 
9.87 311 
9.87 300 

9.87 288 

9.87 277 
9.87 266 
9.87 255 
9.87 243 
9.87 232 

9.87 221 

9.87 209 
9.87 198 
9.87 187 
9.87 175 

9.87 164 
9.87 153 
9.87 141 
9.87 130 
9.87119 
9.87 107 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 

18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 





26 


25 


2 


5.2 


5.0 


3 


7.8 


7.5 


4 


10.4 


10.0 


5 


13.0 


12.5 


6 


15.6 


15.0 


7 


18.2 


17.5 


8 


20.8 


20.0 


9 


23.4 


22.5 




15 


14 


2 


3.0 


2.8 


3 


4.5 


4.2 


4 


6.0 


5.6 


5 


7.5 


7.0 


6 


9.0 


8.4 


7 


10.5 


9.8 


8 


12.0 


11.2 


9 


13.5 


12.6 




12 


11 


2 


2.4 


2.2 


3 


3.6 


3.3 


4 


4.8 


4.4 


5 


6.0 


5.5 


6 


7.2 


6.6 


7 


8.4 


7.7 


8 


9.6 


8.8 


9 


10.8 


9.9 



From the top: 

For41° + or221° + , 
read as printed; for 
131°+ or 311°*, read 
co-function. 

From the hott&m: 

For48 0+ or228 0+ , 
read as printed ; for 
138°+ or 318°+ read 
co-function. 



Prop. Pts. 



48° — Logarithms of Trigonometric Functions 



88 



42° — Logarithms of Trigonometric Functions 



[III 



o 

i 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.82 551 
9.82 565 
9.82 579 
9.82 593 
9.82 607 
9.82 621 
9.82 635 
9.82 649 
9.82 663 
9.82 677 

9.82 691 
9.82 705 
9.82 719 
9.82 733 
9.82 747 
9.82 761 
9.82 775 
9.82 788 
9.82 802 
9.82 816 

9.82 830 
9.82 844 
9.82 858 
9.82 872 
9.82 885 

9.82 899 
9.82 913 
9.82 927 
9.82 941 
9.82 955 

9.82 968 
9.82 982 

9.82 996 

9.83 010 
9.83 023 

9.83 037 
9.83 051 
9.83 065 
9.83 078 
9.83 092 

9.83 106 
9.83 120 
9.83 133 
9.83 147 
9.83 161 

9.83 174 
9.83 188 
9.83 202 
9.83 215 
9.83 229 



.83 242 
.83 256 

.83 270 
.83 283 
.83 297 

.83 310 
.83 324 
.83 338 
.83 351 
.83 365 



9.83 378 



LCos 



14 
14 
14 
14 
14 

14 
14 
14 
14 
14 

14 
14 
14 
14 
14 

14 
13 
14 
14 
14 

14 
14 
14 
13 
14 

14 
14 
14 
14 
13 

14 
14 
14 
13 
14 

14 
14 
13 
14 
14 

14 
13 
14 
14 
13 

14 
14 
13 
14 
13 

14 
14 
13 
14 
13 
14 
14 
13 
14 
13 



L Tan cd 



9.95 
9.95 
9.95 
9.95 
9.95 

9.95 
9.95 
9.95 
9.95 
9.95 

9.95 
9.95 
9.95 
9.95 
9.95 

9.95 
9.95 
9.95 
9.95 
9.95 

9.95 
9.95 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 
9.96 
9.96 
9.96 
9.96 

9.96 



444 
469 
495 
520 
545 

571 

596 
622 
647 
672 

698 
723 

748 
774 
799 

825 
850 
875 
901 
926 
952 
977 
002 
028 
053 

078 
104 
129 
155 
180 

205 
231 
256 
281 
307 
332 
357 
383 
408 
433 

459 
484 
510 
535 
560 

586 
611 
636 
662 

687 
712 
738 
763 
788 
814 

839 
864 
890 
915 
940 
966 



d L Ctn cd 



25 
26 
25 
25 
26 

25 

26 
25 
25 
26 

25 

25 
26 
25 
26 

25 
25 
26 
25 
26 

25 
25 
26 
25 
25 

26 
25 
26 
25 
25 

26 
25 
25 
26 
25 

25 
26 
25 
25 
26 

25 

26 
25 
25 
26 

25 
25 
26 
25 
25 

26 
25 
25 
26 
25 

25 
26 
25 
25 
26 



L Ctn L Cos 



0.04 556 
0.04 531 
0.04 505 
0.04 480 
0.04455 

0.04 429 
0.04 404 
0.04378 
0.04 353 
0.04 328 

0.04 302 
0.04 277 
0.04 252 
0.04 226 
0.04 201 

0.04 175 
0.04 150 
0.04 125 
0.04 099 
0.04 074 

0.04 048 
0.04 023 
0.03 998 
0.03 972 
0.03 947 

0.03 922 
0.03 896 
0.03 871 
0.03 845 
0.03 820 

0.03 795 
0.03 769 
0.03 744 
0.03 719 
0.03 693 

0.03 668 
0.03 643 
0.03 617 
0.03 592 
0.03 567 

0.03 541 
0.03 516 
0.03 490 
0.03 465 
0.03 440 

0.03 414 
0.03 389 
0.03 364 
0.03 338 
0.03 313 

0.03 288 
0.03 262 
0.03 237 
0.03 212 
0.03 186 

0.03 161 
0.03 136 
0.03110 
0.03 085 
0.03 060 

0.03 034 



L Tan L Sin 



9.87 107 
9.87 096 
9.87 085 
9.87 073 
9.87 062 

9.87 050 
9.87 039 
9.87 028 
9.87 016 
9.87 005 

9.86 993 
9.86 982 
9.86 970 
9.86 959 
9.86 947 

9.86 936 
9.86 924 
9.86 913 
9.86 902 
9.86 890 

9.86 879 
9.86 867 
9.86 855 
9.86 844 
9.86 832 
9.86 821 
9.86 809 
9.86 798 
9.86 786 
9.86 775 

9.86 763 
9.86 752 
9.86 740 
9.86 728 
9.86 717 

9.86 705 
9.86 694 
9.86 682 
9.86 670 
9.86 659 

9.86 647 
9.86 635 
9.86 624 
9.86 612 
9.86 600 

9.86 589 
9.86 577 
9.86 565 
9.86 554 
9.86 542 

9.86 530 
9.86 518 
9.86 507 
9.86495 
9.86483 
9.86 472 
9.86460 
9.86448 
9.86436 
9.86 425 
9.86 413 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 




Prop. Pts. 





26 


2 


5.2 


3 


7.8 


4 


10.4 


5 


13.0 


6 


15.6 


7 


18.2 


8 


20.8 


9 


23.4 





14 


2 


2.8 


3 


4.2 


4 


5.6 


5 


7.0 


6 


8.4 


7 


9.8 


8 


11.2 


9 


12.6 





12 


2 


2.4 


3 


3.6 


4 


4.8 


5 


6.0 


6 


7.2 


7 


8.4 


8 


9.6 


9 


10.8 



25 

5.0 
7.5 
10.0 
12.5 
15.0 
17.5 
20.0 
22.5 



13 

2.6 
3.9 
5.2 
6.5 
7.8 
9.1 
10.4 
11.7 



11 

2.2 
3.3 
4.4 
5.5 
6.6 
7.7 
8.8 
9.9 



From the top: 

For42 0+ or222 0+ , 
read as printed ; for 
132 0+ or312 0+ ,read 
co-function. 

From the bottom: 

For47 0+ or227 0+ , 
read as printed; for 
137°+ or 317°+ read 
co-function. 



Prop. Pts. 



47° — Logarithms of Trigonometric Functions 



Ill] 43° — Logarithms of Trigonometric Functions 



89 



o 

i 

2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 

24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.83 378 
9.83 392 
9.83 405 
9.83 419 
9.83 432 

9.83 446 
9.83 459 
9.83 473 
9.83 486 
9.83 500 

9.83 513 
9.83 527 
9.83 540 
9.83 554 
9.83 567 

9.83 581 
9.83 594 
9.83 608 
9.83 621 
9.83 634 

9.83 648 
9.83 661 
9.83 674 
9.83 688 
9.83 701 

9.83 715 
9.83 728 
9.83 741 
9.83 755 
9.83 768 

9.83 781 
9.83 795 
9.83 808 
9.83 821 
9.83 834 



83 848 
.83 861 
83 874 
.83 887 
83 901 

.83 914 
.83 927 
83 940 
83 954 
83 967 

83 980 

83 993 

84 006 
84 020 
84 033 

84 046 
84 059 
84 072 
84 085 
84 098 

84112 
84125 
84138 
84151 
84164 

84177 



LCos 



d L Tan cd 



14 
13 
14 
13 
14 

13 
14 
13 
14 
13 

14 
13 
14 
13 
14 

13 
14 
13 
13 
14 

13 
13 
14 
13 
14 

13 
13 
14 
13 
13 

14 
13 
13 
13 
14 

13 
13 
13 
14 
13 

13 
13 
14 
13 
13 

13 
13 
14 
13 
13 

13 
13 
13 
13 
14 

13 
13 
13 
13 
13 



9.96 
9.96 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.97 
9.97 
9.97 
9.97 

9.97 
9.98 
9.98 
9.98 
9.98 

9.98 
9.98 
9.98 
9.98 
9.98 

9.98 
9.98 
9.98 
9.98 
9.98 

9.98 
9.98 
9.98 
9.98 
9.98 

9.98 



966 
991 
016 
042 
067 
092 
118 
143 
168 
193 

219 
244 
269 
295 
320 

345 
371 
396 
421 
447 
472 
497 
523 
548 
573 

598 
624 
649 
674 
700 

725 
750 

776 
801 
826 

851 
877 
902 
927 
953 

978 
003 
029 
054 
079 

104 
130 
155 
180 
206 

231 

256 
281 
307 
332 

357 

383 
408 
433 
458 

484 



d L Ctn cd 



25 
25 
26 
25 
25 

26 
25 
25 
25 
26 

25 
25 
26 
25 
25 

26 
25 
25 
26 
25 

25 
26 
25 
25 
25 

26 
25 
25 
26 
25 

25 
26 
25 
25 
25 

26 
25 
25 
26 
25 

25 
26 
25 
25 
25 

26 
25 
25 
26 
25 

25 
25 
26 
25 
25 

26 
25 
25 
25 
26 



L Ctn 



0.03 034 
0.03 009 
0.02 984 
0.02 958 
0.02 933 

0.02 908 
0.02 882 
0.02 857 
0.02 832 
0.02 807 
0.02 781 
0.02 756 
0.02 731 
0.02 705 
0.02 680 

0.02 655 
0.02 629 
0.02 604 
0.02 579 
0.02 553 
0.02 528 
0.02 503 
0.02477 
0.02 452 
0.02427 

0.02402 
0.02 376 
0.02 351 
0.02 326 
0.02 300 

0.02 275 
0.02 250 
0.02 224 
0.02 199 
0.02 174 

0.02 149 
0.02 123 
0.02 098 
0.02 073 
0.02 047 

0.02 022 
0.01 997 
0.01971 
0.01 946 
0.01921 

0.01 896 
0.01 870 
0.01 845 
0.01 820 
0.01 794 

0.01 769 
0.01 744 
0.01719 
0.01 693 
0.01668 

0.01 643 
0.01617 
0.01 592 
0.01 567 
0.01 542 

10.01 516 



LTan 



LCos 



9.86 413 
9.86 401 
9.86 389 
9.86 377 
9.86 366 

9.86 354 
9.86 342 
9.86 330 
9.86 318 
9.86 306 

9.86 295 
9.86 283 
9.86 271 
9.86 259 
9.86 247 

9.86 235 
9.86 223 
9.86 211 
9.86 200 
9.86 188 

9.86 176 
9.86 164 
9.86 152 
9.86 140 
9.86 128 

9.86116 
9.86 104 
9.86 092 
9.86 080 
9.86 068 

9.86 056 
9.86 044 
9.86 032 
9.86 020 
9.86 008 

9.85 996 
9.85 984 
9.85 972 
9.85 960 
9.85 948 

9.85 936 
9.85 924 
9.85 912 
9.85 900 
9.85 888 

9.85 876 
9.85 864 
9.85 851 
9.85 839 
9.85 827 

9.85 815 
9.85 803 
9.85 791 
9.85 779 
9.85 766 

9.85 754 
9.85 742 
9.85 730 
9.85 718 
9.85 706 

9.85 693 



LSin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 





26 


25 


2 


5.2 


5.0 


3 


7.8 


7.5 


4 


10.4 


10.0 


5 


13.0 


12.5 


6 


15.6 


15.0 


7 


18.2 


17.5 


8 


20.8 


20.0 


9 


23.4 


22.5 




14 


13 


2 


2.8 


2.6 


3 


4.2 


3.9 


4 


5.6 


5.2 


5 


7.0 


6.5 


6 


8.4 


7.8 


7 


9.8 


9.1 


8 


11.2 


10.4 


9 


12.6 


11.7 




12 


11 


2 


2.4 


2.2 


3 


3.6 


3.3 


4 


4.8 


4.4 


5 


6.0 


5.5 


6 


7.2 


6.6 


7 


8.4 


7.7 


8 


9.6 


8.8 


9 


10.8 


9.9 



From the top: 

For43 0+ or223 0+ , 
read as printed; for 
133°+ or 313°+ read 
co-function. 

From the bottom: 
For 46°+ or 226°+ 
read as printed; for 
136 0+ or316 0+ ,read 
co-function. 



Prop. Pts. 



46° — Logarithms of Trigonometric Functions 



90 



44° — Logarithms of Trigonometric Functions 



[III 



o 

i 

2 
3 
4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 

18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 

48 
49 

50 

51 
52 
53 
54 

55 

56 
57 

58 
59 

60 



LSin 



9.84 177 
9.84 190 
9.84 203 
9.84 216 
9.84 229 

9.84 242 
9.84 255 
9.84 269 
9.84 282 
9.84 295 



.84 308 
.84 321 
.84 334 
.84 347 
.84 360 

.84 373 
.84 385 
.84 398 
.84 411 
.84 424 



9.84 437 
9.84 450 
9.84 463 
9.84 476 
9.84 489 

9.84 502 
9.84 515 
9.84 528 
9.84 540 
9.84 553 

9.84 566 
9.84 579 
9.84 592 
9.84 605 
9.84 618 



.84 630 
.84 643 
.84 656 
.84 669 
.84 682 

.84 694 
.84 707 
.84 720 
.84 733 
.84 745 



9.84 758 
9.84 771 
9.84 784 
9.84 796 
9.84 809 



.84 822 
.84 835 
.84 847 
.84 860 
.84 873 

.84 885 
.84 898 
.84 911 
.84 923 
.84 936 
.84 949 



LCos 



13 
13 
13 
13 
13 

13 
14 
13 
13 
13 

13 
13 
13 
13 
13 

12 
13 
13 
13 
13 

13 
13 
13 
13 
13 

13 
13 
12 
13 
13 

13 
13 
13 
13 
12 

13 

13 
13 
13 
12 

13 
13 
13 
12 
13 

13 
13 
12 
13 
13 

13 
12 
13 
13 
12 

13 
13 
12 
13 
13 



L Tan cd 



9.98 484 
9.98 509 
9.98 534 
9.98 560 
9.98 585 

9.98 610 
9.98 635 
9.98 661 
9.98 686 
9.98 711 

9.98 737 
9.98 762 
9.98 787 
9.98 812 
9.98 838 

9.98 863 
9.98 888 
9.98 913 
9.98 939 
9.98 964 

9.98 989 

9.99 015 
9.99 040 
9.99 065 
9.99 090 

9.99116 
9.99 141 
9.99 166 
9.99 191 
9.99 217 
9.99 242 
9.99 267 
9.99 293 
9.99 318 
9.99 343 

9.99 368 
9.99 394 
9.99 419 
9.99 444 
9.99 469 

9.99 495 
9.99 520 
9.99 545 
9.99 570 
9.99 596 

9.99 621 
9.99 646 
9.99 672 
9.99 697 
9.99 722 

9.99 747 
9.99 773 
9.99 798 
9.99 823 
9.99 848 

9.99 874 
9.99 899 
9.99 924 
9.99 949 
9.99 975 

10.0000 



d L Ctn cd 



25 
25 
26 
25 
25 

25 
26 
25 
25 
26 

25 
25 
25 
26 
25 

25 
25 
26 
25 
25 

26 
25 
25 
25 
26 

25 
25 
25 
26 
25 

25 
26 
25 
25 
25 

26 
25 
25 
25 
26 

25 
25 
25 
26 
25 

25 
26 
25 
25 
25 

26 
25 
25 
25 
26 

25 
25 
25 
26 
25 



LCtn 



0.01516 
0.01491 
0.01 466 
0.01 440 
0.01415 

0.01 390 
0.01 365 
0.01 339 
0.01314 
0.01 289 

0.01 263 
0.01238 
0.01213 
0.01 188 
0.01 162 

0.01 137 
0.01112 
0.01 087 
0.01061 
0.01 036 

0.01011 
0.00 985 
0.00 960 
0.00 935 
0.00 910 

0.00 884 
0.00 859 
0.00 834 
0.00 809 
0.00 783 

0.00 758 
0.00 733 
0.00 707 
0.00 682 
0.00 657 

0.00 632 
0.00 606 
0.00 581 
0.00 556 
0.00 531 

0.00 505 
0.00 480 
0.00 455 
0.00 430 
0.00 404 

0.00 379 
0.00 354 
0.00 328 
0.00 303 
0.00 278 

0.00 253 
0.00 227 
0.00 202 
0.00 177 
0.00 152 

0.00 126 
0.00 101 
0.00 076 
0.00 051 
0.00 025 

10.00 000 



LCos 



9.85 693 
9.85 681 
9.85 669 
9.85 657 
9.85 645 

9.85 632 
9.85 620 
9.85 608 
9.85 596 
9.85 583 

9.85 571 
9.85 559 
9.85 547 
9.85 534 
9.85 522 

9.85 510 
9.85 497 
9.85 485 
9.85 473 
9.85 460 

9.85 448 
9.85 436 
9.85 423 
9.85 411 
9.85 399 

9.85 386 
9.85 374 
9.85 361 
9.85 349 
9.85 337 

9.85 324 
9.85 312 
9.85 299 
9.85 287 
9.85 274 

9.85 262 
9.85 250 
9.85 237 
9.85 225 
9.85 212 

9.85 200 
9.85 187 
9.85 175 
9.85 162 
9.85 150 

9.85 137 
9.85 125 
9.85112 
9.85 100 
9.85 087 

9.85 074 
9.85 062 
9.85 049 
9.85 037 
9.85 024 

9.85 012 
9.84 999 
9.84 986 
9.84 974 
9.84 961 
9.84 949 



L Tan L Sin 



60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 
44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 

28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 





Prop. Pts. 





26 


25 


2 


5.2 


5.0 


3 


7.8 


7.5 


4 


10.4 


10.0 


5 


13.0 


12.5 


6 


15.6 


15.0 


7 


18.2 


17.5 


8 


20.8 


20.0 


9 


23.4 


22.5 




14 


13 


2 


2.8 


2.6 


3 


4.2 


3.9 


4 


5.6 


5.2 


5 


7.0 


6.5 


6 


8.4 


7.8 


7 


9.8 


9.1 


8 


11.2 


10.4 


9 


12.6 


11.7 






12 




2 


2.4 




3 


3.6 




4 


4.8 




5 


6.0 




6 


7.2 




7 


8.4 




8 


9.6 




9 


10.8 



From the top: 
For 44°+ or 224°+ 
read as printed; for 
134°+ or 314°+ read 
co-function. 

From the bottom: 
For45° + or225° + , 
read as printed ; for 
135 0+ or315 0+ ,read 
co-function. 



Prop. Pts. 



45° — Logarithms of Trigonometric Functions 



IV] Table FV 


f 


Degrees, 


Minutes, and Seconds to Radians 91 


Degrees 


Minutes 


Seconds 


0° 


0.00000 00 


60° 


1.04719 76 


120° 


2.09439 51 





0.00000 00 





0.00000 00 


1 


0.01745 33 


61 


1.06465 08 


121 


2.11184 84 


1 


0.00029 09 


1 


0.00000 48 


2 


0.03490 66 


62 


1.08210 41 


122 


2.12930 17 


2 


0.00058 18 


2 


0.00000 97 


3 


0.05235 99 


63 


1.09955 74 


123 


2.14675 50 


3 


0.00087 27 


3 


0.00001 45 


4 


0.06981 32 


64 


1.11701 07 


124 


2.16420 83 


4 


0.00116 36 


4 


0.00001 94 


5 


0.08726 65 


65 


1.13446 40 


125 


2.18166 16 


5 


0.00145 44 


5 


0.00002 42 


6 


0.10471 98 


66 


1.1519173 


126 


2.1991149 


6 


0.00174 53 


6 


0.00002 91 


7 


0.12217 30 


67 


1.16937 06 


127 


2.21656 82 


7 


0.00203 62 


7 


0.00003 39 


8 


0.13962 63 


68 


1.18682 39 


128 


2.23402 14 


8 


0.00232 71 


8 


0.00003 88 


9 


0.15707 96 


69 


1.20427 72 


129 


2.25147 47 


9 


0.00261 80 


9 


0.00004 36 


10 


0.17453 29 


70 


1.22173 05 


130 


2.26892 80 


10 


0.00290 89 


10 


0.00004 85 


11 


0.19198 62 


71 


1.23918 38 


131 


2.28638 13 


11 


0.00319 98 


11 


0.00005 33 


12 


0.20943 95 


72 


1.25663 71 


132 


2.30383 46 


12 


0.00349 07 


12 


0.00005 82 


13 


0.22689 28 


73 


1.27409 04 


133 


2.32128 79 


13 


0.00378 15 


13 


0.00006 30 


14 


0.24434 61 


74 


1.29154 36 


134 


2.33874 12 


14 


0.00407 24 


14 


0.00006 79 


15 


0.26179 94 


75 


1.30899 69 


135 


2.35619 45 


15 


0.00436 33 


15 


0.00007 27 


16 


0.27925 27 


76 


1.32645 02 


136 


2.37364 78 


16 


0.00465 42 


16 


0.00007 76 


17 


0.29670 60 


77 


1.34390 35 


137 


2.39110 11 


17 


0.00494 51 


17 


0.00008 24 


18 


0.31415 93 


78 


1.36135 68 


138 


2.40855 44 


18 


0.00523 60 


18 


0.00008 73 


19 


0.33161 26 


79 


1.37881 01 


139 


2.42600 77 


19 


0.00552 69 


19 


0.00009 21 


20 


0.34906 59 


80 


1.39626 34 


140 


2.44346 10 


20 


0.00581 78 


20 


0.00009 70 


21 


0.36651 91 


81 


1.41371 67 


141 


2.46091 42 


21 


0.00610 87 


21 


0.00010 18 


22 


0.38397 24 


82 


1.43117 00 


142 


2.47836 75 


22 


0.00639 95 


22 


0.00010 67 


23 


0.40142 57 


83 


1.44862 33 


143 


2.49582 08 


23 


0.00669 04 


23 


0.00011 15 


24 


0.41887 90 


84 


1.46607 66 


144 


2.51327 41 


24 


0.00698 13 


24 


0.00011 64 


25 


0.43633 23 


85 


1.48352 99 


145 


2.53072 74 


25 


0.00727 22 


25 


0.00012 12 


26 


0.45378 56 


86 


1.50098 32 


146 


2.54818 07 


26 


0.00756 31 


26 


0.00012 61 


27 


0.47123 89 


87 


1.51843 64 


147 


2.56563 40 


27 


0.00785 40 


27 


0.00013 09 


28 


0.48869 22 


88 


1.53588 97 


148 


2.58308 73 


28 


0.00814 49 


28 


0.00013 57 


29 


0.50614 55 


89 


1.55334 30 


149 


2.60054 06 


29 


0.00843 58 


29 


0.00014 06 


30 


0.52359 88 


90 


1.57079 63 


150 


2.61799 39 


30 


0.00872 66 


30 


0.00014 54 


31 


0.54105 21 


91 


1.58824 96 


151 


2.63544 72. 


31 


0.00901 75 


31 


0.00015 03 


32 


0.55850 54 


92 


1.60570 29 


152 


2.65290 05 


32 


0.00930 84 


32 


0.00015 51 


33 


0.57595 87 


93 


1.62315 62 


153 


2.67035 38 


33 


0.00959 93 


33 


0.00016 00 


34 


0.59341 19 


94 


1.64060 95 


154 


2.68780 70 


34 


0.00989 02 


34 


0.00016 48 


35 


0.61086 52 


95 


1.65806 28 


155 


2.70526 03 


35 


0.01018 11 


35 


0.00016 97 


36 


0.62831 85 


96 


1.67551 61 


156 


2.72271 36 


36 


0.01047 20 


36 


0.00017 45 


37 


0.64577 18 


97 


1.69296 94 


157 


2.74016 69 


37 


0.01076 29 


37 


0.00017 94 


38 


0.66322 51 


98 


1.71042 27 


158 


2.75762 02 


38 


0.01105 38 


38 


0.00018 42 


39 


0.68067 84 


99 


1.72787 60 


159 


2.77507 35 


39 


0.01134 46 


39 


0.00018 91 


40 


0.69813 17 


100 


1.74532 93 


160 


2.79252 68 


40 


0.01163 55 


40 


0.00019 39 


41 


0.71558 50 


101 


1.76278 25 


161 


2.80998 01 


41 


0.01192 64 


41 


0.00019 88 


42 


0.73303 83 


102 


1.78023 58 


162 


2.82743 31 


42 


0.01221 73 


42 


0.00020 36 


43 


0.75049 16 


103 


1.79768 91 


163 


2.84488 67 


43 


0.01250 82 


43 


0.00020 85 


44 


0.76794 49 


104 


1.81514 24 


164 


2.86234 00 


44 


0.01279 91 


44 


0.00021 33 


45 


0.78539 82 


105 


1.83259 57 


165 


2.87979 33 


45 


0.01309 00 


45 


0.00021 82 


46 


0.80285 15 


106 


1.85004 90 


166 


2.89724 66 


46 


0.01338 09 


46 


0.00022 30 


47 


0.82030 47 


107 


1.86750 23 


167 


2.91469 99 


47 


0.01367 17 


47 


0.00022 79 


48 


0.83775 80 


108 


1.88495 56 


168 


2.93215 31 


48 


0.01396 26 


48 


0.00023 27 


49 


0.85521 13 


109 


1.90240 89 


169 


2.94960 64 


49 


0.01425 35 


49 


0.00023 76 


50 


0.87266 46 


110 


1.91986 22 


170 


2.96705 97 


50 


0.01454 44 


50 


0.00024 24 


51 


0.89011 79 


111 


1.93731 55 


171 


2.98451 30 


51 


0.01483 53 


51 


0.00024 73 


52 


0.90757 12 


112 


1.95476 88 


172 


3.00196 63 


52 


0.01512 62 


52 


0.00025 21 


53 


0.92502 45 


113 


1.97222 21 


173 


3.01941 96 


53 


0.01541 71 


53 


0.00025 70 


54 


0.94247 78 


114 


1.98967 53 


174 


3.03687 29 


54 


0.01570 80 


54 


0.00026 18 


55 


0.95993 11 


115 


2.00712 86 


175 


3.05432 62 


55 


0.01599 89 


55 


0.00026 66 


56 


0.97738 44 


116 


2.02458 19 


176 


3.07177 95 


56 


0.01628 97 


56 


0.00027 15 


57 


0.99483 77 


117 


2.04203 52 


177 


3.08923 28 


57 


0.01658 06 


57 


0.00027 63 


58 


1.01229 10 


118 


2.05948 85 


178 


3.10668 61 


58 


0.01687 15 


58 


0.00028 12 


59 


1.02974 43 


119 


2.07694 18 


179 


3.12413 94 


59 


0.01716 24 


59 


0.00028 60 


60 


1.04719 76 


120 


2.09439 51 


180 


3.14159 27 


60 


0.01745 33 


60 


0.00029 09 



92 Table V — Radian Measure — Trigonometric Functions [V 



CO 

3 

a 


Sin * 


Cos * 


Tan* 


Equivalent 
of* 


.00 


.00000 


1.0000 


.00000 


0° OO'.O 


.01 
.02 
.03 

.04 
.05 
.06 

.07 
.08 
.09 


.01000 
.02000 
.03000 

.03999 
.04998 
.05996 

.06994 
.07991 

.08988 


.99995 
.99980 
.99955 

.99920 
.99875 
.99820 

.99755 
.99680 
.99595 


.01000 
.02000 
.03001 

.04002 
.05004 
.06007 

.07011 
.08017 
.09024 


0° 34'.4 
1° 08'.8 
1° 43'.1 

2° 17'.5 
2° 51'.9 
3° 26'.3 

4° 00'.6 
4° 35'.0 
5° 09'.4 


.10 


.09983 


.99500 


.10033 


5° 43'.8 


.11 
.12 
.13 

.14 
.15 
.16 

.17 
.18 
.19 


.10978 
.11971 
.12963 

.13954 
.14944 
.15932 

.16918 
.17903 

.18886 


.99396 
.99281 
.99156 

.99022 

.98877 
.98723 

.98558 
.98384 
.98200 


.11045 
.12058 
.13074 

.14092 
.15114 
.16138 

.17166 
.18197 
.19232 


6° 18'.2 
6° 52'.5 
7° 26'.9 

8° 01'.3 
8° 35'.7 
9° lO'.O 

9° 44'.4 
10° 18'.8 
10° 53'.2 


.20 


.19867 


.98007 


.20271 


11° 27'.5 


.21 
.22 
.23 

.24 
.25 
.26 

.27 

.28 
.29 


.20846 
.21823 
.22798 

.23770 
.24740 
.25708 

.26673 
.27636 
.28595 


.97803 
.97590 
.97367 

.97134 
.96891 
.96639 

.96377 
.96106 
.95824 


.21314 
.22362 
.23414 

.24472 
.25534 
.26602 

.27676 
.28755 
.29841 


12° or.9 

12° 36'.3 
13° 10'.7 

13°45M 

14° 19'.4 
14° 53'.8 

15° 28'.2 
16° 02'.6 
16° 36'.9 


.30 


.29552 


.95534 


.30934 


17° ir.3 


.31 
.32 
.33 

.34 
.35 
.36 

.37 

.38 
.39 


.30506 
.31457 
.32404 

.33349 
.34290 
.35227 

.36162 
.37092 
.38019 


.95233 
.94924 
.94604 

.94275 
.93937 
.93590 

.93233 

.92866 
.92491 


.32033 
.33139 
.34252 

.35374 
.36503 
.37640 

.38786 
.39941 
.41105 


17° 45'.7 
18° 20M 
18° 54'.5 

19° 28'.8 
20° 03'.2 
20° 37'.6 

21° 12'.0 
21° 46'.3 
22° 20'.7 


.40 


.38942 


.92106 


.42279 


22° 55U 


.41 
.42 
.43 

.44 
.45 
.46 

.47 
.48 
.49 


.39861 
.40776 
.41687 

.42594 
.43497 
.44395 

.45289 
.46178 
.47063 


.91712 
.91309 
.90897 

.90475 
.90045 
.89605 

.89157 
.88699 
.88233 


.43463 
.44657 
.45862 

.47078 
.48306 
.49545 

.50797 
.52061 
.53339 


23° 29'.5 
24° 03'.9 
24° 38'.2 

25° 12'.6 
25° 47'.0 
26° 21'.4 

26° 55\7 

27° 30M 
28° 04'.5 


.50 


.47943 


.87758 


.54630 


28° 38'.9 



1 


Sin x 


Cos x 


Tan* 


Equivalent 
of* 


.50 


.47943 


.87758 


.54630 


28° 38'.9 


.51 
.52 
.53 

.54 
.55 
.56 

.57 

.58 
.59 


.48818 
.49688 
.50553 

.51414 
.52269 
.53119 

.53963 
.54802 
.55636 


.87274 
.86782 
.86281 

.85771 
.85252 

.84726 

.84190 
.83646 
.83094 


.55936 
.57256 
.58592 

.59943 
.61311 
.62695 

.64097 
.65517 
.66956 


29° 13'.3 
29° 47'.6 
30° 22'.0 

30° 56'.4 
31°30'.8 
32° 05'.1 

32° 39'.5 
33° 13'.9 
33° 48'.3 


.60 


.56464 


.82534 


.68414 


34° 22'.6 


.61 
.62 
.63 

.64 
.65 
.66 

.67 

.68 
.69 


.57287 
.58104 
.58914 

.59720 
.60519 
.61312 

.62099 
.62879 
.63654 


.81965 

.81388 
.80803 

.80210 
.79608 
.78999 

.78382 
.77757 
.77125 


.69892 
.71391 
.72911 

.74454 
.76020 
.77610 

.79225 
.80866 
.82534 


34° 57'.0 
35° 31'.4 
36° 05'.8 

36° 40'.2 
37° 14'.5 
37° 48'.9 

38° 23'.3 
38° 57'.7 
39° 32'.0 


.70 


.64422 


.76484 


.84229 


40° 06'.4 


.71 

.72 
.73 

.74 
.75 
.76 

.77 
.78 
.79 


.65183 
.65938 
.66687 

.67429 
.68164 

.68892 

.69614 
.70328 
.71035 


.75836 
.75181 
.74517 

.73847 
.73169 

.72484 

.71791 
.71091 
.70385 


.85953 
.87707 
.89492 

.91309 
.93160 
.95045 

.96967 
.98926 
1.0092 


40° 40'.8 
41° 15'.2 
41°49'.6 

42° 23'.9 
42° 58'.3 
43° 32'.7 

44°07M 
44° 41'.4 
45° 15'.8 


.80 


.71736 


.69671 


1.0296 


45° 50'.2 


.81 
.82 
.83 

.84 

.85 
.86 

.87 
.88 
.89 


.72429 
.73115 
.73793 

.74464 
.75128 

.75784 

.76433 

.77074 

.77707 


.68950 
.68222 

.67488 

.66746 
.65998 
.65244 

.64483 
.63715 
.62941 


1.0505 
1.0717 
1.0934 

1.1156 
1.1383 
1.1616 

1.1853 
1.2097 
1.2346 


46° 24'.6 
46° 59'.0 
47° 33'.3 

48° 07'.7 
48° 42M 
49° 16'.5 

49° 50'.8 
50° 25 r .2 
50° 59'.6 


.90 


.78333 


.62161 


1.2602 


51°34'.0 


.91 
.92 
.93 

.94 
.95 
.96 

.97 
.98 
.99 


.78950 
.79560 
.80162 

.80756 
.81342 
.81919 

.82489 
.83050 
.83603 


.61375 
.60582 
.59783 

.58979 
.58168 
.57352 

.56530 
.55702 

.54869 


1.2864 
1.3133 
1.3409 

1.3692 
1.3984 
1.4284 

1.4592 
1.4910 
1.5237 


52° 08'.3 
52° 42'.7 
53° 17M 

53° 51'.5 
54° 25'.9 
55° 00^2 

55° 34'.6 
56° 09'.0 
56° 43'.4 


1.00 


.84147 


.54030 


1.5574 


57° 17'.7 



V] 


Radian Measure — Trigonometric Functions 


93 


BO 

1 

a 


Sin x 


Cos x 


Tana; 


•fca 
g 


CO 
03 

H 


Sin x 


Cos x 


Tana; 


C 

3 

13 H 

> «M 

•s ° 

a* 


1.00 


.84147 


.54030 


1.5574 


57° 17'.7 


1.30 


.96356 


.26750 


3.6021 


74°29M 


1.01 
1.02 
1.03 

1.04 
1.05 
1.06 

1.07 
1.08 
1.09 


.84683 
.85211 
.85730 

.86240 
.86742 
.87236 

.87720 
.88196 
.88663 


.53186 
.52337 
.51482 

.50622 
.49757 

.48887 

.48012 
.47133 
.46249 


1.5922 
1.6281 
1.6652 

1.7036 
1.7433 
1.7844 

1.8270 
1.8712 
1.9171 


57° 52'.1 
58° 26'.5 
59° 00'.9 

59° 35'.3 
60° 09'.6 
60° 44'.0 

61° 18'.4 
61° 52'.8 
62° 27'.1 


1.31 
1.32 
1.33 

1.34 
1.35 
1.36 

1.37 
1.38 
1.39 


.96618 
.96872 
.97115 

.97348 
.97572 

.97786 

.97991 
.98185 
.98370 


.25785 
.24818 
.23848 

.22875 
.21901 
.20924 

.19945 
.18964 
.17981 


3.7471 
3.9033 
4.0723 

4.2556 
4.4552 
4.6734 

4.9131 
5.1774 
5.4707 


75° 08'.4 
75° 37'.8 
76° 12'.2 

76° 46'.6 
77° 21'.0 
77° 55'.3 

78° 29'.7 
79° 04U 
79° 38'.5 


1.10 


.89121 


.45360 


1.9648 


63° 01'.5 


1.40 


.98545 


.16997 


5.7979 


80° 12'.8 


1.11 
1.12 
1.13 

1.14 
1.15 
1.16 

1.17 
1.18 
1.19 


.89570 
.90010 
.90441 

.90863 
.91276 
.91680 

.92075 
.92461 
.92837 


.44466 
.43568 
.42666 

.41759 
.40849 
.39934 

.39015 
.38092 
.37166 


2.0143 
2.0660 
2.1198 

2.1759 
2.2345 
2.2958 

2.3600 
2.4273 
2.4979 


63° 35'.9 
64° 10'.3 
64° 44'.7 

65° 19'.0 
65° 53'.4 

66° 27'.8 

67° 02'.2 
67° 36'.5 
68° 10'.9 


1.41 
1.42 
1.43 

1.44 
1.45 
1.46 

1.47 
1.48 
1.49 


.98710 
.98865 
.99010 

.99146 
.99271 
.99387 

.99492 
.99588 
.99674 


.16010 
.15023 
.14033 

.13042 
.12050 
.11057 

.10063 
.09067 
.08071 


6.1654 
6.5811 
7.0555 

7.6018 
8.2381 
8.9886 

9.8874 
10.983 
12.350 


80° 47\2 
81° 21'.6 
81° 56'.0 

82° 30'.4 
83° 04'.7 
83° 39'.1 

84° 13'.5 
84° 47'.9 
85° 22'.2 


1.20 


.93204 


.36236 


2.5722 


68° 45'.3 


1.50 


.99749 


.07074 


14.101 


85° 56'.6 


1.21 
1.22 
1.23 

1.24 
1.25 
1.26 

1.27 
1.28 
1.29 


.93562 
.93910 
.94249 

.94578 
.94898 
.95209 

.95510 
.95802 
.96084 


.35302 
.34365 
.33424 

.32480 
.31532 
.30582 

.29628 
.28672 
.27712 


2.6503 

2.7328 
2.8198 

2.9119 
3.0096 
3.1133 

3.2236 
3.3413 
3.4672 


69° 19'.7 
69° 54U 
70° 28'.4 

71° 02'.8 
71° 37'.2 
72° 11'.6 

72° 45'.9 
73° 20'.3 
73° 54'.7 


1.51 
1.52 
1.53 

1.54 
1.55 
1.56 

•1.57 


.99815 
.99871 
.99917 

.99953 
.99978 
.99994 

♦1.0000 


.06076 
.05077 
.04079 

.03079 
.02079 
.01080 

*.00080 


16.428 
19.670 
24.498 

32.461 

48.078 
92.621 

*1255.8 


86° 31'.0 
87° 05'.4 
87° 39'.8 

88° 14'. 1 

88° 48'.5 
89° 22'.9 

89° 57'.3 


1.58 
1.59 


.99996 
.99982 


-.00920 
-.01920 


-108.65 
-52.067 


90° 31'.6 
91° O^.O 


1.30 


.96356 


.26750 


3.6021 


74°29'.l 


1.60 


.99957 


-.02920 


-34.233 


91° 40'.4 



7T radians = 180° 1 radian = 57° 17' 44".806 - 57.°2957795 

7T = 3.14159265 3600'' = 60' - 1° = O.01745329 radian 

*1 right angle = 90° = tt/2 radians - 1.5707963 radians 



Table Va — Radians to Degrees 





Radians 


Tenths 


Hundredths 


Thousandths 


Ten-thousandths 


1 


57°17 / 44 ,, .8 


5°43 , 46 /, .5 


0°34'22 ,/ .6 


0° 3'26".3 


0° 0'20".6 


2 


114°35 , 29 ,, .6 


11°27 , 33 ,, .0 


1° 8'45".3 


0° 6 , 52 /, .5 


0° O^l"^ 


3 


171°53 , 14 ,/ .4 


17°11 , 19 ,, .4 


1°43 , 07 ,, .9 


0°10 , 18 ,, .8 


0° 1'01".9 


4 


229°10 , 59".2 


22 o 55'05 r/ .9 


2°17'30".6 


0°13'45 ,/ .l 


0° 1'22 ,, .5 


5 


286°28'44 ,, .0 


28°38 , 52 ,, .4 


2°51 , 53 ,, .2 


0°17'11".3 


0° 1'43'M 


6 


343°46'28 ,, .8 


34°22 / 38 ,/ .9 


Z°2Q'\b"$ 


0°20 , 37".6 


0° 2 , 03".8 


7 


401° 4'13".6 


40° 6'25".4 


4° 0'W.b 


0°24 , 03 ,, .9 


0° 2 , 24 , '.4 


8 


458°21 , 58 ,, .4 


45°50 , 11 ,, .8 


4°35'01 // .2 


0°27 , 30 ,, .l 


0° 2 , 45 /, .0 


9 


sis^g^"^ 


51°33 , 58 ,, .3 


5° &2Z".% 


WSOWA 


0° 3 , 05 ,/ .6 



94 


Table VI 


— Powers — I 


loots — 


• Reciprocals 


[VI 


n 


n 2 


V^ 


VlOn 


n 3 


-\fn 


non 


ShLOO n 


l/n 1 


1.00 


1.0000 


1.00000 


3.16228 


1.00000 


1.00000 


2.15443 


4.64159 


1.00000 


1.01 
1.02 
1.03 

1.04 
1.05 
1.06 

1.07 
1.08 
1.09 


1.0201 
1.0404 
1.0609 

1.0816 
1.1025 
1.1236 

1.1449 
1.1664 
1.1881 


1.00499 
1.00995 
1.01489 

1.01980 
1.02470 
1.02956 

1.03441 
1.03923 
1.04403 


3.17805 
3.19374 
3.20936 

3.22490 
3.24037 
3.25576 

3.27109 
3.28634 
3.30151 


1.03030 
1.06121 
1.09273 

1.12486 
1.15762 
1.19102 

1.22504 
1.25971 
1.29503 


1.00332 
1.00662 
1.00990 

1.01316 
1.01640 
1.01961 

1.02281 
1.02599 
1.02914 


2.16159 
2.16870 
2.17577 

2.18279 
2.18976 
2.19669 

2.20358 
2.21042 
2.21722 


4.65701 
4.67233 
4.68755 

4.70267 
4.71769 
4.73262 

4.74746 
4.76220 

4.77686 


.990099 
.980392 
.970874 

.961538 
.952381 
.943396 

.934579 
.925926 
.917431 


1.10 


1.2100 


1.04881 


3.31662 


1.33100 


1.03228 


2.22398 


4.79142 


.909091 


1.11 
1.12 
1.13 

1.14 
1.15 
1.16 

1.17 
1.18 
1.19 


1.2321 
1.2544 
1.2769 

1.2996 
1.3225 
1.3456 

1.3689 
1.3924 
1.4161 


1.05357 
1.05830 
1.06301 

1.06771 
1.07238 
1.07703 

1.08167 
1.08628 
1.09087 


3.33167 
3.34664 
3.36155 

3.37639 
3.39116 
3.40588 

3.42053 
3.43511 
3.44964 


1.36763 
1.40493 
1.44290 

1.48154 
1.52088 
1.56090 

1.60161 
1.64303 
1.68516 


1.03540 
1.03850 
1.04158 

1.04464 
1.04769 
1.05072 

1.05373 
1.05672 
1.05970 


2.23070 
2.23738 
2.24402 

2.25062 
2.25718 
2.26370 

2.27019 
2.27664 
2.28305 


4.80590 
4.82028 
4.83459 

4.84881 
4.86294 
4.87700 

4.89097 
4.90487 
4.91868 


.900901 

.892857 
.884956 

.877193 
.869565 
.862069 

.854701 
.847458 
.840336 


1.20 


1.4400 


1.09545 


3.46410 


1.72800 


1.06266 


2.28943 


4.93242 


.833333 


1.21 
1.22 
1.23 

1.24 
1.25 
1.26 

1.27 
1.28 
1.29 


1.4641 
1.4884 
1.5129 

1.5376 
1.5625 
1.5876 

1.6129 
1.6384 
1.6641 


1.10000 
1.10454 
1.10905 

1.11355 
1.11803 
1.12250 

1.12694 
1.13137 
1.13578 


3.47851 
3.49285 
3.50714 

3.52136 
3.53553 
3.54965 

3.56371 
3.57771 
3.59166 


1.77156 
1.81585 
1.86087 

1.90662 
1.95312 
2.00038 

2.04838 
2.09715 
2.14669 


1.06560 
1.06853 
1.07144 

1.07434 
1.07722 
1.08008 

1.08293 

1.08577 
1.08859 


2.29577 
2.30208 
2.30835 

2.31459 
2.32079 
2.32697 

2.33311 
2.33921 
2.34529 


4.94609 
4.95968 
4.97319 

4.98663 
5.00000 
5.01330 

5.02653 
5.03968 
5.05277 


.826446 
.819672 
.813008 

.806452 
.800000 
.793651 

.787402 
.781250 
.775194 


1.30 


1.6900 


1.14018 


3.60555 


2.19700 


1.09139 


2.35133 


5.06580 


.769231 


1.31 
1.32 
1.33 

1.34 
1.35 
1.36 

1.37 
1.38 
1.39 


1.7161 
1.7424 
1.7689 

1.7956 
1.8225 
1.8496 

1.8769 
1.9044 
1.9321 


1.14455 
1.14891 
1.15326 

1.15758 
1.16190 
1.16619 

1.17047 
1.17473 

1.17898 


3.61939 
3.63318 
3.64692 

3.66060 
3.67423 
3.68782 

3.70135 
3.71484 

3.72827 


2.24809 
2.29997 
2.35264 

2.40610 
2.46038 
2.51546 

2.57135 

2.62807 
2.68562 


1.09418 
1.09696 
1.09972 

1.10247 
1.10521 
1.10793 

1.11064 
1.11334 
1.11602 


2.35735 
2.36333 
2.36928 

2.37521 
2.38110 
2.38697 

2.39280 
2.39861 
2.40439 


5.07875 
5.09164 
5.10447 

5.11723 
5.12993 
5.14256 

5.15514 
5.16765 
5.18010 


.763359 
.757576 
.751880 

.746269 
.740741 
.735294 

.729927 
.724638 
.719424 


1.40 


1.9600 


1.18322 


3.74166 


2.74400 


1.11869 


2.41014 


5.19249 


.714286 


1.41 
1.42 
1.43 

1.44 
1.45 
1.46 

1.47 

1.48 
1.49 


1.9881 
2.0164 
2.0449 

2.0736 
2.1025 
2.1316 

2.1609 
2.1904 
2.2201 


1.18743 
1.19164 
1.19583 

1.20000 
1.20416 
1.20830 

1.21244 
1.21655 
1.22066 


3.75500 
3.76829 
3.78153 

3.79473 

3.80789 
3.82099 

3.83406 

3.84708 
3.86005 


2.80322 
2.86329 
2.92421 

2.98598 
3.04862' 
3.11214 

3.17652 
3.24179 
3.30795 


1.12135 
1.12399 
1.12662 

1.12924 
1.13185 
1.13445 

1.13703 
1.13960 
1.14216 


2.41587 
2.42156 
2:42724 

2.43288 
2.43850 
2.44409 

2.44966 
2.45520 
2.46072 


5.20483 
5.21710 
5.22932 

5.24148 
5.25359 
5.26564 

5.27763 

5.28957 
5.30146 


.709220 
.704225 
.699301 

.694444 
.689655 
.684932 

.680272 
.675676 
.671141 


1.50 


2.2500 


1.22474 


3.87298 


3.37500 


1.14471 


2.46621 


5.31329 


.666667 


n 


n 2 


V^ 


VlOn 


n 3 


-yfn 


^10 n 


^100 n 


l/n 



VI] 




Po 


wers — 


Roots - 


— Reciprocals 




95 


n 


n 2 


Vn 


VlOn 


n 3 


yln 


^10 n 


S/lOOn 


1/n 1 


1.50 


2.2500 


1.22474 


3.87298 


3.37500 


1.14471 


2.46621 


5.31329 


.666667 


1.51 
1.52 
1.53 

1.54 
1.55 
1.56 

1.57 
1.58 
1.59 


2.2801 
2.3104 
2.3409 

2.3716 
2.4025 
2.4336 

2.4649 
2.4964 
2.5281 


1.22882 
1.23288 
1.23693 

1.24097 
1.24499 
1.24900 

1.25300 
1.25698 
1.26095 


3.88587 
3.89872 
3.91152 

3.92428 
3.93700 
3.94968 

3.96232 
3.97492 

3.98748 


3.44295 
3.51181 
3.58158 

3.65226 
3.72388 
3.79642 

3.86989 
3.94431 
4.01968 


1.14725 

1.14978 
1.15230 

1.15480 
1.15729 
1.15978 

1.16225 
1.16471 
1.16717 


2.47168 
2.47712 
2.48255 

2.48794 
2.49332 
2.49867 

2.50399 
2.50930 
2.51458 


5.32507 
5.33680 
5.34848 

5.36011 
5.37169 
5.38321 

5.39469 
5.40612 
5.41750 


.662252 
.657895 
.653595 

.649351 
.645161 
.641026 

.636943 
.632911 
.628931 


3.60 


2.5600 


1.26491 


4.00000 


4.09600 


1.16961 


2.51984 


5.42884 


.625000 


1.61 
1.62 
1.63 

1.64 
1.65 
1.66 

1.67 

1.68 
1.69 


2.5921 
2.6244 
2.6569 

2.6896 
2.7225 
2.7556 

2.7889 
2.8224 
2.8561 


1.26886 
1.27279 
1.27671 

1.28062 
1.28452 
1.28841 

1.29228 
1.29615 
1.30000 


4.01248 
4.02492 
4.03733 

4.04969 
4.06202 
4.07431 

4.08656 
4.09878 
4.11096 


4.17328 
4.25153 
4.33075 

4.41094 
4.49212 
4.57430 

4.65746 
4.74163 
4.82681 


1.17204 
1.17446 
1.17687 

1.17927 
1.18167 
1.18405 

1.18642 
1.18878 
1.19114 


2.52508 
2.53030 
2.53549 

2.54067 
2.54582 
2.55095 

2.55607 
2.56116 
2.56623 


5.44012 
5.45136 
5.46256 

5.47370 

5.48481 
5.49586 

5.50688 
5.51785 
5.52877 


.621118 
.617284 
.613497 

.609756 
.606061 
.602410 

.598802 
.595238 
.591716 


1.70 


2.8900 


1.30384 


4.12311 


4.91300 


1.19348 


2.57128 


5.53966 


.588235 


1.71 
1.72 
1.73 

1.74 
1.75 
1.76 

1.77 

1.78 
1.79 


2.9241 
2.9584 
2.9929 

3.0276 
3.0625 
3.0976 

3.1329 
3.1684 
3.2041 


1.30767 
1.31149 
1.31529 

1.31909 
1.32288 
1.32665 

1.33041 
1.33417 
1.33791 


4.13521 
4.14729 
4.15933 

4.17133 
4.18330 
4.19524 

4.20714 
4.21900 
4.23084 


5.00021 
5.08845 
5.17772 

5.26802 
5.35938 
5.45178 

5.54523 
5.63975 
5.73534 


1.19582 
1.19815 
1.20046 

1.20277 
1.20507 
1.20736 

1.20964 
1.21192 
1.21418 


2.57631 
2.58133 
2.58632 

2.59129 
2.59625 
2.60118 

2.60610 
2.61100 
2.61588 


5.55050 
5.56130 
5.57205 

5.58277 
5.59344 
5.60408 

5.61467 
5.62523 
5.63574 


.584795 
581395 
.578035 

.574713 
.571429 
.568182 

.564972 
.561798 
.558659 


1.80 


3.2400 


1.34164 


4.24264 


5.83200 


1.21644 


2.62074 


5.64622 


.555556 


1.81 
1.82 
1.83 

1.84 
1.85 
1.86 

1.87 
1.88 
1.89 


3.2761 
3.3124 
3.3489 

3.3856 
3.4225 
3.4596 

3.4969 
3.5344 
3.5721 


1.34536 
1.34907 
1.35277 

1.35647 
1.36015 
1.36382 

1.36748 
1.37113 
1.37477 


4.25441 
4.26615 
4.27785 

4.28952 
4.30116 
4.31277 

4.32435 
4.33590 
4.34741 


5.92974 
6.02857 
6.12849 

6.22950 
6.33162 
6.43486 

6.53920 
6.64467 
6.75127 


1.21869 
1.22093 
1.22316 

1.22539 
1.22760 
1.22981 

1.23201 
1.23420 
1.23639 


2.62559 
2.63041 
2.63522 

2.64001 
2.64479 
2.64954 

2.65428 
2.65901 
2.66371 


5.65665 
5.66705 
5.67741 

5.68773 
5.69802 
5.70827 

5.71848 
5.72865 
5.73879 


.552486 
.549451 
.546448 

.543478 
.540541 
.537634 

.534759 
.531915 
.529101 


1.90 


3.6100 


1.37840 


4.35890 


6.85900 


1.23856 


2.66840 


5.74890 


.526316 


1.91 
1.92 
1.93 

1.94 
1.95 
1.96 

1.97 
1.98 
1.99 


3.6481 
3.6864 
3.7249 

3.7636 
3.8025 
3.8416 

3.8809 
3.9204 
3.9601 


1.38203 
1.38564 
1.38924 

1.39284 
1.39642 
1.40000 

1.40357 
1.40712 
1.41067 


4.37035 
4.38178 
4.39318 

4.40454 
4.41588 
4.42719 

4.43847 
4.44972 
4.46094 


6.96787 
7.07789 
7.18906 

7.30138 

7.41488 
7.52954 

7.64537 
7.76239 
7.88060 


1.24073 
1.24289 
1.24505 

1.24719 
1.24933 
1.25146 

1.25359 
1.25571 
1.25782 


2.67307 
2.67773 
2.68237 

2.68700 
2.69161 
2.69620 

2.70078 
2.70534 
2.70989 


5.75897 
5.76900 
5.77900 

5.78896 
5.79889 
5.80879 

5.81865 
5.82848 

5.83827 


.523560 
.520833 
.518135 

.515464 
.512821 
.510204 

.507614 
.505051 
.502513 


2.00 


4.0000 


1.41421 


4.47214 


8.00000 


1.25992 


2.71442 


5.84804 


.500000 


n 


n 2 


V^ 


VlOn 


n 3 


^ 


^10 n 


^100 n 


1/n 



96 




Powers — 


Roots - 


— Reciprocals 




[VI 


n 


71 2 


Vra 


VlOfi 


n 3 


ifn 


y/l0n 


VlOO n 


1/n 


2.00 


4.0000 


1.41421 


4.47214 


8.00000 


1.25992 


2.71442 


5.84804 


.500000 


2.01 
2.02 
2.03 

2.04 
2.05 
2.06 

2.07 
2.08 
2.09 


4.0401 
4.0804 
4.1209 

4.1616 
4.2025 
4.2436 

4.2849 
4.3264 
4.3681 


1.41774 
1.42127 

1.42478 

1.42829 
1.43178 
1.43527 

1.43875 
1.44222 
1.44568 


4.48330 
4.49444 
4.50555 

4.51664 
4.52769 
4.53872 

4.54973 
4.56070 
4.57165 


8.12060 
8.24241 
8.36543 

8.48966 
8.61512 

8.74182 

8.86974 
8.99891 
9.12933 


1.26202 
1.26411 
1.26619 

1.26827 
1.27033 
1.27240 

1.27445 
1.27650 
1.27854 


2.71893 
2.72344 
2.72792 

2.73239 
2.73685 
2.74129 

2.74572 
2.75014 
2.75454 


5.85777 
5.86746 
5.87713 

5.88677 
5.89637 
5.90594 

5.91548 
5.92499 
5.93447 


.497512 
.495050 
.492611 

.490196 
.487805 
.485437 

.483092 
.480769 
.478469 


2.10 


4.4100 


1.44914 


4.58258 


9.26100 


1.28058 


2.75892 


5.94392 


.476190 


2.11 
2.12 
2.13 

2.14 
2.15 
2.16 

2.17 

2.18 
2.19 


4.4521 
4.4944 
4.5369 

4.5796 
4.6225 
4.6656 

4.7089 
4.7524 
4.7961 


1.45258 
1.45602 
1.45945 

1.46287 
1.46629 
1.46969 

1.47309 
1.47648 
1.47986 


4.59347 
4.60435 
4.61519 

4.62601 
4.63681 
4.64758 

4.65833 
4.66905 
4.67974 


9.39393 
9.52813 
9.66360 

9.80034 
9.93838 
10.0777 

10.2183 
10.3602 
10.5035 


1.28261 
1.28463 
1.28665 

1.28866 
1.29066 
1.29266 

1.29465 
1.29664 
1.29862 


2.76330 
2.76766 
2.77200 

2.77633 
2.78065 
2.78495 

2.78924 
2.79352 
2.79779 


5.95334 
5.96273 
5.97209 

5.98142 
5.99073 
6.00000 

6.00925 
6.01846 
6.02765 


.473934 
.471698 
.469434 

.467290 
.465116 
.462963 

.460829 
.458716 
.456621 


2.20 


4.8400 


1.48324 


4.69042 


10.6480 


1.30059 


2.80204 


6.03681 


.454545 


2.21 
2.22 
2.23 

2.24 
2.25 
2.26 

2.27 
2.28 
2.29 


4.8841 
4.9284 
4.9729 

5.0176 
5.0625 
5.1076 

5.1529 
5.1984 
5.2441 


1.48661 
1.48997 
1.49332 

1.49666 
1.50000 
1.50333 

1.50665 
1.50997 
1.51327 


4.70106 
4.71169 
4.72229 

4.73286 
4.74342 
4.75395 

4.76445 
4.77493 
4.78539 


10.7939 
10.9410 
11.0896 

11.2394 
11.3906 
11.5432 

11.6971 
11.8524 
12.0090 


1.30256 
1.30452 
1.30648 

1.30843 
1.31037 
1.31231 

1.31424 
1.31617 
1.31809 


2.80628 
2.81050 

2.81472 

2.81892 
2.82311 

2.82728 

2.83145 
2.83560 
2.83974 


6.04594 
6.05505 
6.06413 

6.07318 
6.08220 
6.09120 

6.10017 
6.10911 
6.11803 


.452489 
.450450 
.448430 

.446429 
.444444 
.442478 

.440529 
.438596 
.436681 


2.30 


5.2900 


1.51658 


4.79583 


12.1670 


1.32001 


2.84387 


6.12693 


.434783 


2.31 
2.32 
2.33 

2.34 
2.35 
2.36 

2.37 
2.38 
2.39 


5.3361 
5.3824 
5.4289 

5.4756 
5.5225 
5.5696 

5.6169 
5.6644 
5.7121 


1.51987 
1.52315 
1.52643 

1.52971 
1.53297 
1.53623 

1.53948 
1.54272 
1.54596 


4.80625 
4.81664 
4.82701 

4.83735 

4.84768 
4.85798 

4.86826 

4.87852 
4.88876 


12.3264 
12.4872 
12.6493 

12.8129 
12.9779 
13.1443 

13.3121 
13.4813 
13.6519 


1.32192 
1.32382 
1.32572 

1.32761 
1.32950 
1.33139 

1.33326 
1.33514 
1.33700 


2.84798 
2.85209 
2.85618 

2.86026 
2.86433 
2.86838 

2.87243 
2.87646 
2.88049 


6.13579 
6.14463 
6.15345 

6.16224 
6.17101 
6.17975 

6.18846 
6.19715 
6.20582 


.432900 
.431034 
.429185 

.427350 
.425532 
.423729 

.421941 
.420168 
.418410 


2.40 


5.7600 


1.54919 


4.89898 


13.8240 


1.33887 


2.88450 


6.21447 


.416667 


2.41 

2.42 
2.43 

2.44 
2.45 
2.46 

2.47 
2.48 
2.49 


5.8081 
5.8564 
5.9049 

5.9536 
6.0025 
6.0516 

6.1009 
6.1504 
6.2001 


1.55242 
1.55563 
1.55885 

1.56205 
1.56525 
1.56844 

1.57162 
1.57480 
1.57797 


4.90918 
4.91935 
4.92950 

4.93964 
4.94975 
4.95984 

4.96991 
4.97996 
4.98999 


13.9975 
14.1725 
14.3489 

14.5268 
14.7061 
14.8869 

15.0692 
15.2530 
15.4382 


1.34072 
1.34257 
1.34442 

1.34626 
1.34810 
1.34993 

1.35176 
1.35358 
1.35540 


2.88850 
2.89249 
2.89647 

2.90044 
2.90439 
2.90834 

2.91227 
2.91620 
2.92011 


6.22308 
6.23168 
6.24025 

6.24880 
6.25732 
6.26583 

6.27431 
6.28276 
6.29119 


.414938 
.413223 
.411523 

.409836 
.408163 
.406504 

.404858 
.403226 
.401606 


2.50 


6.2500 


1.58114 


5.00000 


15.6250 


1.35721 


2.92402 


6.29961 


.400000 


n 


n 2 


Vn 


VlOn 


n 3 


yfn 


^10 n 


<l\00n 


1/n 



VI] 




Powers — 


Roots - 


— Reciprocals 




97 


n 


n 2 


Vri 










1/n 


VlOn 


n 3 


In 


VlOn 


VlOOn 


2.50 


6.2500 


1.58114 


5.00000 


15.6250 


1.35721 


2.92402 


6.29961 


.400000 


2.51 
2.52 
2.53 

2.54 
2.55 
2.56 

2.57 

2.58 
2.59 


6.3001 
6.3504 
6.4009 

6.4516 
6.5025 
6.5536 

6.6049 
6.65.64 
6.7081 


1.58430 
1.58745 
1.59060 

1.59374 

1.59687 
1.60000 

1.60312 
1.60624 
1.60935 


5.00999 
5.01996 
5.02991 

5.03984 
5.04975 
5.05964 

5.06952 
5.07937 
5.08920 


15.8133 
16.0030 
16.1943 

16.3871 
16.5814 
16.7772 

16.9746 
17.1735 
17.3740 


1.35902 
1.36082 
1.36262 

1.36441 
1.36620 
1.36798 

1.36976 
1.37153 
1.37330 


2.92791 
2.93179 
2.93567 

2.93953 
2.94338 
2.94723 

2.95106 
2.95488 
2.95869 


6.30799 
6.31636 
6.32470 

6.33303 
6.34133 
6.34960 

6.35786 
6.36610 
6.37431 


.398406 
.396825 
.395257 

.393701 
.392157 
.390625 

.389105 
.387597 
.386100 


2.60 


6.7600 


1.61245 


5.09902 


17.5760 


1.37507 


2.96250 


6.38250 


.384615 


2.61 
2.62 
2.63 

2.64 
2.65 
2.66 

2.67 
2.68 
2.69 


6.8121 
6.8644 
6.9169 

6.9696 
7.0225 
7.0756 

7.1289 
7.1824 
7.2361 


1.61555 
1.61864 
1.62173 

1.62481 

1.62788 
1.63095 

1.63401 
1.63707 
1.64012 


5.10882 
5.11859 
5.12835 

5.13809 
5.14782 
5.15752 

5.16720 
5.17687 
5.18652 


17.7796 
17.9847 
18.1914 

18.3997 
18.6096 
18.8211 

19.0342 

19.2488 
19.4651 


1.37683 
1.37859 
1.38034 

1.38208 
1.38383 
1.38557 

1.38730 
1.38903 
1.39076 


2.96629 
2.97007 
2.97385 

2.97761 
2.98137 
2.98511 

2.98885 
2.99257 
2.99629 


6.39068 
6.39883 
6.40696 

6.41507 
6.42316 
6.43123 

6.43928 
6.44731 
6.45531 


.383142 
.381679 
.380228 

.378788 
.377358 
.375940 

.374532 
.373134 
.371747 


2.70 


7.2900 


1.64317 


5.19615 


19.6830 


1.39248 


3.00000 


6.46330 


.370370 


2.71 
2.72 
2.73 

2.74 
2.75 
2.76 

2.77 
2.78 
2.79 


7.3441 
7.3984 
7.4529 

7.5076 
7.5625 
7.6176 

7.6729 

7.7284 
7.7841 


1.64621 
1.64924 
1.65227 

1.65529 
1.65831 
1.66132 

1.66433 
1.66733 
1.67033 


5.20577 
5.21536 
5.22494 

5.23450 
5.24404 
5.25357 

5.26308 
5.27257 
5.28205 


19.9025 
20.1236 
20.3464 

20.5708 
20.7969 
21.0246 

21.2539 
21.4850 
21.7176 


1.39419 
1.39591 
1.39761 

1.39932 
1.40102 
1.40272 

1.40441 
1.40610 
1.40778 


3.00370 
3.00739 
3.01107 

3.01474 
3.01841 
3.02206 

3.02570 
3.02934 
3.03297 


6.47127 
6.47922 
6.48715 

6.49507 
6.50296 
6.51083 

6.51868 
6.52652 
6.53434 


.369004 
.367647 
.366300 

.364964 
.363636 
.362319 

.361011 
.359712 
.358423 


2.80 


7.8400 


1.67332 


5.29150 


21.9520 


1.40946 


3.03659 


6.54213 


.357143 


2.81 
2.82 
2.83 

2.84 
2.85 
2.86 

2.87 
2.88 
2.89 


7.8901 
7.9524 
8.0089 

8.0656 
8.1225 
8.1796 

8.2369 
8.2944 
8.3521 


1.67631 
1.67929 
1.68226 

1.68523 

1.68819 
1.69115 

1.69411 
1.69706 
1.70000 


5.30094 
5.31037 
5.31977 

5.32917 
5.33854 
5.34790 

5.35724 

5.36656 
5.37587 


22.1880 
22.4258 
22.6652 

22.9063 
23.1491 
23.3937 

23.6399 
23.8879 
24.1376 


1.41114 
1.41281 
1.41448 

1.41614 
1.41780 
1.41946 

1.42111 

1.4z276 
1.42440 


3.04020 
3.04380 
3.04740 

3.05098 
3.05456 
3.05813 

3.06169 
3.06524 

3.06878 


6.54991 
6.55767 
6.56541 

6.57314 
6.58084 
6.58853 

6.59620 
6.60385 
6.61149 


.355872 
.354610 
.353357 

.352113 
.350877 
.349650 

.348432 
.347222 
.346021 


2.90 


8.4100 


1.70294 


5.38516 


24.3890 


1.42604 


3.07232 


6.61911 


.344828 


2.91 
2.92 
2.93 

2.94 
2.95 
2.96 

2.97 

2.98 
2.99 


8.4681 
8.5264 
8.5849 

8.6436 
8.7025 
8.7616 

8.8209 
8.8804 
8.9401 


1.70587 
1.70880 
1.71172 

1.71464 
1.71756 
1.72047 

1.72337 
1.72627 
1.72916 


5.39444 
5.40370 
5.41295 

5.42218 
5.43139 
5.44059 

5.44977 
5.45894 
5.46809 


24.6422 
24.8971 
25.1538 

25.4l'22 
25.6724 
25.9343 

26.1981 
26.4636 
26.7309 


1.42768 
1.42931 
1.43094 

1.43257 
1.43419 
1.43581 

1.43743 
1.43904 
1.44065 


3.07584 
3.07936 
3.08287 

3.08638 
3.08987 
3.09336 

3.09684 
3.10031 
3.10378 


6.62671 
6.63429 
6.64185 

6.64940 
6.65693 
6.66444 

6.67194 
6.67942 

6.68688 


.343643 
.342466 
.341297 

.340136 
.338983 
.337838 

.336700 
.335570 
.334448 


3.00 


9.0000 


1.73205 


5.47723 


27.0000 


1.44225 


3.10723 


6.69433 


.333333 


n 


n 2 


Vn 




n 3 


-\fn 






1/n 


VlOn 


^10 n 


^100 n 






98 




Pot 


vers — 


Roots - 


- Reciprocals 




[VI 


n 


n 2 


Vn 


VlOn 


n 3 


Jn 


^10 n 


yllOOn 


l/n 


3.00 


9.0000 


1.73205 


5.47723 


27.0000 


1.44225 


3.10723 


6.69433 


.333333 


3.01 
3.02 
3.03 

3.04 
3.05 
3.06 

3.07 
3.08 
3.09 


9.0601 
9.1204 
9.1809 

9.2416 
9.3025 
9.3636 

9.4249 
9.4864 
9.5481 


1.73494 
1.73781 
1.74069 

1.74356 
1.74642 
1.74929 

1.75214 
1.75499 

1.75784 


5.48635 
5.49545 
5.50454 

5.51362 
5.52268 
5.53173 

5.54076 
5.54977 
5.55878 


27.2709 
27.5436 

27.8181 

28.0945 
28.3726 
28.6526 

28.9344 
29.2181 
29.5036 


1.44385 
1.44545 
1.44704 

1.44863 
1.45022 
1.45180 

1.45338 
1.45496 
1.45653 


3.11068 
3.11412 
3.11756 

3.12098 
3.12440 
3.12781 

3.13121 
3.13461 
3.13800 


6.70176 
6.70917 
6.71657 

6.72395 
6.73132 
6.73866 

6.74600 
6.75331 
6.76061 


.332226 
.331126 
.330033 

.328947 
.327869 
.326797 

.325733 
.324675 
.323625 


3.10 


9.6100 


1.76068 


5.56776 


29.7910 


1.45810 


3.14138 


6.76790 


.322581 


3.11 
3.12 
3.13 

3.14 
3.15 
3.16 

3.17 
3.18 
3.19 


9.6721 
9.7344 
9.7969 

9.8596 
9.9225 
9.9856 

10.0489 
10.1124 
10.1761 


1.76352 
1.76635 
1.76918 

1.77200 
1.77482 
1.77764 

1.78045 
1.78326 
1.78606 


5.57674 
5.58570 
5.59464 

5.60357 
5.61249 
5.62139 

5.63028 
5.63915 
5.64801 


30.0802 
30.3713 
30.6643 

30.9591 
31.2559 
31.5545 

31.8550 
32.1574 
32.4618 


1.45967 
1.46123 
1.46279 

1.46434 
1.46590 
1.46745 

1.46899 
1.47054 
1.47208 


3.14475 
3.14812 
3.15148 

3.15483 
3.15818 
3.16152 

3.16485 
3.16817 
3.17149 


6.77517 
6.78242 
6.78966 

6.79688 
6.80409 
6.81128 

6.81846 
6.82562 
6.83277 


.321543 
.320513 
.319489 

.318471 
.317460 
.316456 

.315457 
.314465 
.313480 


3.20 


10.2400 


1.78885 


5.65685 


32.7680 


1.47361 


3.17480 


6.83990 


.312500 


3.21 
3.22 
3.23 

3.24 
3.25 
3.26 

3.27 
3.28 
3.29 


10.3041 
10.3684 
10.4329 

10.4976 
10.5625 
10.6276 

10.6929 
10.7584 
10.8241 


1.79165 
1.79444 
1.79722 

1.80000 
1.80278 
1.80555 

1.80831 
1.81108 
1.81384 


5.66569 
5.67450 
5.68331 

5.69210 
5.70088 
5.70964 

5.71839 
5.72713 
5.73585 


33.0762 
33.3862 
33.6983 

34.0122 
34.3281 
34.6460 

34.9658 
35.2876 
35.6113 


1.47515 

1.47668 
1.47820 

1.47973 
1.48125 
1.48277 

1.48428 
1.48579 
1.48730 


3.17811 
3.18140 
3.18469 

3.18798 
3.19125 
3.19452 

3.19778 
3.20104 
3.20429 


6.84702 
6.85412 
6.86121 

6.86829 
6.87534 
6.88239 

6.88942 
6.89643 
6.90344 


.311526 
.310559 
.309598 

.308642 
.307692 
.306748 

.305810 
.304878 
.303951 


3.30 


10.8900 


1.81659 


5.74456 


35.9370 


1.48881 


3.20753 


6.91042 


.303030 


3.31 
3.32 
3.33 

3.34 
3.35 
3.36 

3.37 
3.38 
3.39 


10.9561 
11.0224 
11.0889 

11.1556 
11.2225 
11.2896 

11.3569 
11.4244 
11.4921 


1.81934 
1.82209 
1.82483 

1.82757 
1.83030 
1.83303 

1.83576 

1.83848 
1.84120 


5.75326 
5.76194 
5.77062 

5.77927 
5.78792 
5.79655 

5.80517 
5.81378 
5.82237 


36.2647 
36.5944 
36.9260 

37.2597 
37.5954 
37.9331 

38.2728 
38.6145 
38.9582 


1.49031 
1.49181 
1.49330 

1.49480 
1.49629 
1.49777 

1.49926 
1.50074 
1.50222 


3.21077 
3.21400 
3.21722 

3.22044 
3.22365 
3.22686 

3.23006 
3.23325 
3.23643 


6.91740 
6.92436 
6.93130 

6.93823 
6.94515 
6.95205 

6.95894 
6.96582 
6.97268 


.302115 
.301205 
.300300 

.299401 
.298507 
.297619 

.296736 
.295858 
.294985 


3.40 


11.5600 


1.84391 


5.83095 


39.3040 


1.50369 


3.23961 


6.97953 


.294118 


3.41 
3.42 
3.43 

3.44 
3.45 
3.46 

3.47 
3.48 
3.49 


11.6281 
11.6964 
11.7649 

11.8336 
11.9025 
11.9716 

12.0409 
12.1104 
12.1801 


1.84662 
1.84932 
1.85203 

1.85472 
1.85742 
1.86011 

1.86279 
1.86548 
1.86815 


5.83952 
5.84808 
5.85662 

5.86515 
5.87367 

5.88218 

5.89067 
5.89915 
5.90762 


39.6518 
40.0017 
40.3536 

40.7076 
41.0636' 
41.4217 

41.7819 
42.1442 
42.5085 


1.50517 
1.50664 
1.50810 

1.50957 
1.51103 
1.51249 

1.51394 
1.51540 
1.51685 


3.24278 
3.24595 
3.24911 

3.25227 
3.25542 
3.25856 

3.26169 
3.26482 
3.26795 


6.98637 
6.99319 
7.00000 

7.00680 
7.01358 
7.02035 

7.02711 
7.03385 
7.04058 


.293255 
.292398 
.291545 

.290698 
.289855 
.289017 

.288184 
.287356 
.286533 


3.50 


12.2500 


1.87083 


5.91608 


42.8750 


1.51829 


3.27107 


7.04730 


.285714 


n 


n 2 


V^ 




n 3 


1Z 






l/n 


VlOn 


^10 n 


y/lOOn 



VI] 




Powers — 


Roots - 


— Reciprocals 




99 


n 


n 2 


v^ 




n 3 


m 






l/n 


VlOn 


illOn 


\100n 


3.50 


12.2500 


1.87083 


5.91608 


42.8750 


1.51829 


3.27107 


7.04730 


.285714 


3.51 
3.52 
3.53 

3.54 
3.55 
3.56 

3.57 
5.58 
3.59 


12.3201 
12.3904 
12.4609 

12.5316 
12.6025 
12.6736 

12.7449 
12.8164 

12.8881 


1.87350 
1.87617 

1.87883 

1.88149 
1.88414 
1.88680 

1.88944 
1.89209 
1.89473 


5.92453 
5.93296 
5.94138 

5.94979 
5.95819 
5.96657 

5.97495 
5.98331 
5.99166 


43.2436 
43.6142 
43.9870 

44.3619 
44.7389 
45.1180 

45.4993 

45.8827 
46.2683 


1.51974 
1.52118 
1.52262 

1.52406 
1.52549 
1.52692 

1.52835 

1.52978 
1.53120 


3.27418 
3.27729 
3.28039 

3.28348 
3.28657 
3.28965 

3.29273 
3.29580 

3.29887 


7.05400 
7.06070 
7.06738 

7.07404 
7.08070 
7.08734 

7.09397 
7.10059 
7.10719 


.284900 
.284091 
.283286 

.282486 
.281690 
.280899 

.280112 
.279330 
.278552 


3.60 


12.9600 


1.89737 


6.00000 


46.6560 


1.53262 


3.30193 


7.11379 


.277778 


3.61 
3.62 
3.63 

3.64 
3.65 
3.66 

3.67 
3.68 
3.69 


13.0321 
13.1044 
13.1769 

13.2496 
13.3225 
13.3956 

13.4689 
13.5424 
13.6161 


1.90000 
1.90263 
1.90526 

1.90788 
1.91050 
1.91311 

1.91572 
1.91833 
1.92094 


6.00833 
6.01664 
6.02495 

6.03324 
6.04152 
6.04979 

6.05805 
6.06630 
6.07454 


47.0459 
47.4379 
47.8321 

48.2285 
48.6271 
49.0279 

49.4309 
49.8360 
50.2434 


1.53404 
1.53545 
1.53686 

1.53827 
1.53968 
1.54109 

1.54249 
1.54389 
1.54529 


3.30498 
3.30803 
3.31107 

3.31411 
3.31714 
3.32017 

3.32319 
3.32621 
3.32922 


7.12037 
7.12694 
7.13349 

7.14004 
7.14657 
7.15309 

7.15960 
7.16610 
7.17258 


.277008 
.276243 

.275482 

.274725 
.273973 
.273224 

.272480 
.271739 
.271003 


3.70 


13.6900 


1.92354 


6.08276 


50.6530 


1.54668 


3.33222 


7.17905 


.270270 


3.71 
3.72 
3.73 

3.74 
3.75 
3.76 

3.77 

3.78 
3.79 


13.7641 
13.8384 
13.9129 

13.9876 
14.0625 
14.1376 

14.2129 

14.2884 
14.3641 


1.92614 
1.92873 
1.93132 

1.93391 
1.93649 
1.93907 

1.94165 
1.94422 
1.94679 


6.09098 
6.09918 
6.10737 

6.11555 
6.12372 
6.13188 

6.14003 
6.14817 
6.15630 


51.0648 
51.4788 
51.8951 

52.3136 
52.7344 
53.1574 

53.5826 
54.0102 
54.4399 


1.54807 
1.54946 
1.55085 

1.55223 
1.55362 
1.55500 

1.55637 
1.55775 
1.55912 


3.33522 
3.33822 
3.34120 

3.34419 
3.34716 
3.35014 

3.35310 
3.35607 
3.35902 


7.18552 
7.19197 
7.19840 

7.20483 
7.21125 
7.21765 

7.22405 
7.23043 
7.23680 


.269542 
.268817 
.268097 

.267380 
.266667 
.265957 

.265252 
.264550 
.263852 


3.80 


14.4400 


1.94936 


6.16441 


54.8720 


1.56049 


3.36198 


7.24316 


.263158 


3.81 
3.82 
3.83 

3.84 
3.85 
3.86 

3.87 

3.88 
3.89 


14.5161 
14.5924 
14.6689 

14.7456 
14.8225 
14.8996 

14.9769 
15.0544 
15.1321 


1.95192 
1.95448 
1.95704 

1.95959 
1.96214 
1.96469 

1.96723 
1.96977 
1.97231 


6.17252 
6.18061 
6.18870 

6.19677 
6.20484 
6.21289 

6.22093 
6.22896 
6.23699 


55.3063 
55.7430 
56.1819 

56.6231 
57.0666 
57.5125 

57.9606 
58.4111 
58.8639 


1.56186 
1.56322 
1.56459 

1.56595 
1.56731 
1.56866 

1.57001 
1.57137 
1.57271 


3.36492 
3.36786 
3.37080 

3.37373 
3.37666 
3.37958 

3.38249 
3.38540 
3.38831 


7.24950 
7.25584 
7.26217 

7.26848 
7.27479 
7.28108 

7.28736 
7.29363 
7.29989 


.262467 
.261780 
.261097 

.260417 
.259740 
.259067 

.258398 
.257732 
.257069 


3.90 


15.2100 


1.97484 


6.24500 


59.3190 


1.57406 


3.39121 


7.30614 


.256410 


3.91 
3.92 
3.93 

3.94 
3.95 
3.96 

3.97 
3.98 
3.99 


15.2881 
15.3664 
15.4449 

15.5236 
15.6025 
15.6816 

15.7609 
15.8404 
15.9201 


1.97737 
1.97990 
1.98242 

1.98494 
1.98746 
1.98997 

1.99249 
1.99499 
1.99750 


6.25300 
6.26099 
6.26897 

6.27694 
6.28490 
6.29285 

h 6.30079 
6.30872 
6.31664 


59.7765 
60.2363 
60.6985 

61.1630 
61.6299 
62.0991 

62.5708 
63.0448 
63.5212 


1.57541 
1.57675 
1.57809 

1.57942 
1.58076 
1.58209 

1.58342 
1.58475 
1.58608 


3.39411 
3.39700 
3.39988 

3.40277 
3.40564 
3.40851 

3.41138 
3.41424 
3.41710 


7.31238 
7.31861 
7.32483 

7.33104 
7.33723 
7.34342 

7.34960 
7.35576 
7.36192 


.255754 
.255102 
.254453 

.253807 
.253165 
.252525 

.251889 
.251256 
.250627 


4.00 


16.0000 


2.00000 


6.32456 


64.0000 


1.58740 


3.41995 


7.36806 


.250000 


n 


n 2 


Vn 




n 3 


yfn 






l/n 


VlOn 


^10 n 


^100 n| 



100 




Powers — 


Roots - 


- Reciprocals 




[VI 


n 


n 2 


Vn 




n 3 


^n 




l/n 


VlOn 


illOn 


VlOOn 


4.00 


16.0000 


2.00000 


6.32456 


64.0000 


1.58740 


3.41995 


7.36806 


.250000 


4.01 
4.02 
4.03 

4.04 
4.05 
4.06 

4.07 
4.08 
4.09 


16.0801 
16.1604 
16.2409 

16.3216 
16.4025 
16.4836 

16.5649 
16.6464 
16.7281 


2.00250 
2.00499 
2.00749 

2.00998 
2.01246 
2.01494 

2.01742 
2.01990 
2.02237 


6.33246 
6.34035 
6.34823 

6.35610 
6.36396 
6.37181 

6.37966 
6.38749 
6.39531 


64.4812 
64.9648 
65.4508 

65.9393 
66.4301 
66.9234 

67.4191 
67-9173 
68.4179 


1.58872 
1.59004 
1.59136 

1.59267 
1.59399 
1.59530 

1.59661 
1.59791 
1.59922 


3.42280 
3.42564 
3.42848 

3.43131 
3.43414 
3.43697 

3.43979 
3.44260 
3.44541 


7.37420 
7.38032 
7.38644 

7.39254 
7.39864 
7.40472 

7.41080 
7.41686 
7.42291 


.249377 
.248756 
.248139 

.247525 
.246914 
.246305 

.245700 
.245098 
.244499 


4.10 


16.8100 


2.02485 


6.40312 


68.9210 


1.60052 


3.44822 


7.42896 


.243902 


4.11 
4.12 
4.13 

4.14 
4.15 
4.16 

4.17 
4.18 
4.19 


16.8921 
16.9744 
17.0569 

17.1396 
17.2225 
17.3056 

17.3889 
17.4724 
17.5561 


2.02731 
2.02978 
2.03224 

2.03470 
2.03715 
2.03961 

2.04206 
2.04450 
2.04695 


6.41093 
6.41872 
6.42651 

6.43428 
6.44205 
6.44981 

6.45755 
6.46529 
6.47302 


69.4265 
69.9345 
70.4450 

70.9579 
71.4734 
71.9913 

72.5117 
73.0346 
73.5601 


1.60182 
1.60312 
1.60441 

1.60571 
1.60700 
1.60829 

1.60958 
1.61086 
1.61215 


3.45102 
3.45382 
3.45661 

3.45939 
3.46218 
3.46496 

3.46773 
3.47050 
3.47327 


7.43499 
7.44102 
7.44703 

7.45304 
7.45904 
7.46502 

7.47100 

7.47697 
7.48292 


.243309 
.242718 
.242131 

.241546 
.240964 
.240385 

.239808 
.239234 
.238663 


4.20 


17.6400 


2.04939 


6.48074 


74.0880 


1.61343 


3.47603 


7.48887 


.238095 


4.21 
4.22 
4.23 

4.24 
4.25 
4.26 

4.27 

4.28 
4.29 


17.7241 

17.8084 
17.8929 

17.9776 
18.0625 
18.1476 

18.2329 
18.3184 
18.4041 


2.05183 
2.05426 
2.05670 

2.05913 
2.06155 
2.06398 

2.06640 

2.06882 
2.07123 


6.48845 
6.49615 
6.50384 

6.51153 
6.51920 
6.52687 

6.53452 
6.54217 
6.54981 


74.6185 
75.1514 
75.6870 

76.2250 
76.7656 

77.3088 

77.8545 
78.4028 
78.9536 


1.61471 
1.61599 
1.61726 

1.61853 
1.61981 
1.62108 

1.62234 
1.62361 

1.62487 


3.47878 
3.48154 
3.48428 

3.48703 
3.48977 
3.49250 

3.49523 
3.49796 
3.50068 


7.49481 
7.50074 
7.50666 

7.51257 
7.51847 
7.52437 

7.53025 
7.53612 
7.54199 


.237530 
.236967 
.236407 

.235849 
.235294 
.234742 

.234192 
.233645 
.233100 


4.30 


18.4900 


2.07364 


6.55744 


79.5070 


1.62613 


3.50340 


7.54784 


.232558 


4.31 
4.32 
4.33 

4.34 
4.35 
4.36 

4.37 
4.38 
4.39 


18.5761 
18.6624 
18.7489 

18.8356 
18.9225 
19.0096 

19.0969 
19.1844 
19.2721 


2.07605 
2.07846 
2.08087 

2.08327 
2.08567 
2.08806 

2.09045 
2.09284 
2.09523 


6.56506 
6.57267 
6.58027 

6.58787 
6.59545 
6.60303 

6.61060 
6.61816 
6.62571 


80.0630 
80.6216 

81.1827 

81.7465 
82.3129 
82.8819 

83.4535 
84.0277 
84.6045 


1.62739 
1.62865 
1.62991 

1.63116 
1.63241 
1.63366 

1.63491 
1.63619 
1.63740 


3.50611 
3.50882 
3.51153 

3.51423 
3.51692 
3.51962 

3.52231 
3.52499 
3.52767 


7.55369 
7.55953 
7.56535 

7.57117 
7.57698 

7.58279 

7.58858 
7.59436 
7.60014 


.232019 
.231481 
.230947 

.230415 

.229885 
.229358 

.228833 
.228311 
.227790 


4.40 


19.3600 


2.09762 


6.63325 


85.1840 


1.63864 


3.53035 


7.60590 


.227273 


4.41 
4.42 
4.43 

4.44 
4.45 
4.46 

4.47 

4.48 
4.49 


19.4481 
19.5364 
19.6249 

19.7136 
19.8025 
19.8916 

19.9809 
20.0704 
20.1601 


2.10000 
2.10238 
2.10476 

2.10713 

2.10950 
2.11187 

2.11424 

2.11660 

2.11896 


6.64078 
6.64831 
6.65582 

6.66333 
6.67083 
6.67832 

6.68581 
6.69328 
6.70075 


85.7661 
86.3509 
86.9383 

87.5284 
88.1211 
88.7165 

89.3146 
89.9154 
90.5188 


1.63988 
1.64112 
1.64236 

1.64359 
1.64483 
1.64606 

1.64729 
1,64851 
1.64974 


3.53302 
3.53569 
3.53835 

3.54101 
3.54367 
3.54632 

3.54897 
3.55162 
3.55426 


7.61166 
7.61741 
7.62315 

7.62888 
7.63461 
7.64032 

7.64603 
7.65172 
7.65741 


.226757 
.226244 
.225734 

.225225 
.224719 
.224215 

.223714 
.223214 
.222717 


4.50 


20.2500 


2.12132 


6.70820 


91.1250 


1.65096 


3.55689 


7.66309 


.222222 


« n 


n 2 


Vn 


VlOn 


tt 3 


yfn 


^10 n 


^100 n 


l/n 



VI] 




Powers — 


Roots - 


— Reciprocals 




101 


n 


n 2 


Vn 


VlOn 


n 3 


In 


non 


VlOOn 


1/n 


4.50 


20.2500 


2.12132 


6.70820 


91.1250 


1.65096 


3.55689 


7.66309 


.222222 


4.51 
4.52 
4.53 

4.54 
4.55 
4.56 

4.57 
4.58 
4.59 


20.3401 
20.4304 
20.5209 

20.6116 
20.7025 
20.7936 

20.8849 
20.9764 
21.0681 


2.12368 
2.12603 
2.12838 

2.13073 
2.13307 
2.13542 

2.13776 

2.14009 
2.14243 


6.71565 
6.72309 
6.73053 

6.73795 
6.74537 

6.75278 

6.76018 
6.76757 
6.77495 


91.7339 
92.3454 
92.9597 

93.5767 
94.1964 
94.8188 

95.4440 
96.0719 
96.7026 


1.65219 
1.65341 
1.65462 

1.65584 
1.65706 
1.65827 

1.65948 
1.66069 
1.66190 


3.55953 
3.56215 
3.56478 

3.56740 
3.57002 
3.57263 

3.57524 
3.57785 
3.58045 


7.66877 
7.67443 
7.68009 

7.68573 
7.69137 
7.69700 

7.70262 
7.70824 
7.71384 


.221729 
.221239 
.220751 

.220264 
.219780 
.219298 

.218818 
.218341 
.217865 


4.60 


21.1600 


2.14476 


6.78233 


97.3360 


1.66310 


3.58305 


7.71944 


.217391 


4.61 
4.62 
4.63 

4.64 
4.65 
4.66 

4.67 
4.68 
4.69 


21.2521 
21.3444 
21.4369 

21.5296 
21.6225 
21.7156 

21.8089 
21.9024 
21.9961 


2.14709 
2.14942 
2.15174 

2.15407 
2.15639 
2.15870 

2.16102 
2.16333 
2.16564 


6.78970 
6.79706 
6.80441 

6.81175 
6.81909 
6.82642 

6.83374 
6.84105 
6.84836 


97.9722 
98.6111 
99.2528 

99.8973 
100.545 
101.195 

101.848 
102.503 
103.162 


1.66431 
1.66551 
1.66671 

1.66791 
1.66911 
1.67030 

1.67150 

1.67269 
1.67388 


3.58564 
3.58823 
3.59082 

3.59340 
3.59598 
3.59856 

3.60113 
3.60370 
3.60626 


7.72503 
7.73061 
7.73619 

7.74175 
7.74731 

7.75286 

7.75840 
7.76394 
7.76946 


.216920 
.216450 

.215983 

.215517 
.215054 
.214592 

.214133 
.213675 
.213220 


4.70 


22.0900 


2.16795 


6.85565 


103.823 


1.67507 


3.60883 


7.77498 


.212766 


4.71 

4.72 
4.73 

4.74 
4.75 
4.76 

4.77 
4.78 
4.79 


22.1841 
22.2784 
22.3729 

22.4676 
22.5625 
22.6576 

22.7529 

22.8484 
22.9441 


2.17025 
2.17256 

2.17486 

2.17715 
2.17945 
2.18174 

2.18403 
2.18632 
2.18861 


6.86294 
6.87023 
6.87750 

6.88477 
6.89202 
6.89928 

6.90652 
6.91375 
6.92098 


104.487 
105.154 
105.824 

106.496 
107.172 
107.850 

108.531 
109.215 
109.902 


1.67626 
1.67744 
1.67863 

1.67981 
1.68099 
1.68217 

1.68334 
1.68452 
1.68569 


3.61138 
3.61394 
3.61649 

3.61903 
3.62158 
3.62412 

3.62665 
3.62919 
3.63172 


7.78049 
7.78599 
7.79149 

7.79697 
7.80245 
7.80793 

7.81339 

7.81885 
7.82429 


.212314 
.211864 
.211416 

.210970 
.210526 
.210084 

.209644 
.209205 

.208768 


4.80 


23.0400 


2.19089 


6.92820 


110.592 


1.68687 


3.63424 


7.82974 


.208333 


4.81 
4.82 
4.83 

4.84 
4.85 
4.86 

4.87 
4.88 
4.89 


23.1361 
23.2324 
23.3289 

23.4256 
23.5225 
23.6196 

23.7169 
23.8144 
23.9121 


2.19317 
2.19545 
2.19773 

2.20000 
2.20227 
2.20454 

2.20681 
2.20907 
2.21133 


6.93542 
6.94262 
6.94982 

6.95701 
6.96419 
6.97137 

6.97854 
6.98570 
6.99285 


111.285 
111.980 
112.679 

113.380 
114.084 
114.791 

115.501 
116.214 
116.930 


1.68804 
1.68920 
1.69037 

1.69154 
1.69270 
1.69386 

1.69503 
1.69619 
1.69734 


3.63676 
3.63928 
3.64180 

3.64431 

3.64682 
3.64932 

3.65182 
3.65432 
3.65681 


7.83517 
7.84059 
7.84601 

7.85142 

7.85683 
7.86222 

7.86761 
7.87299 

7.87837 


.207900 
.207469 
.207039 

.206612 
.206186 
.205761 

.205339 
.204918 
.204499 


4.90 


24.0100 


2.21359 


7.00000 


117.649 


1.69850 


3.65931 


7.88374 


.204082 


4.91 
4.92 
4.93 

4.94 
4.95 
4.96 

4.97 
4.98 
4.99 


24.1081 
24.2064 
24.3049 

24.4036 
24.5025 
24.6016 

24.7009 
24.8004 
24.9001 


2.21585 
2.21811 
2.22036 

2.22261 
2.22486 
2.22711 

2.22935 
2.23159 
2.23383 


7.00714 
7.01427 
7.02140 

7.02851 
7.03562 
7.04273 

7.04982 
7.05691 
7.06399 


118.371 
119.095 
119.823 

120.554 
121.287 
122.024 

122.763 
123.506 
124.251 


1.69965 
1.70081 
1.70196 

1.70311 
1.70426 
1.70540 

1.70655 
1.70769 

1.70884 


3.66179 
3.66428 
3.66676 

3.66924 
3.67171 
3.67418 

3.67665 
3.67911 
3.68157 


7.88909 
7.89445 
7.89979 

7.90513 
7.91046 
7.91578 

7.92110 
7.92641 
7.93171 


.203666 
.203252 
.202840 

.202429 
.202020 
.201613 

.201207 
.200803 
.200401 


5.00 


25.0000 


2.23607 


7.07107 


125.000 


1.70998 


3.68403 


7.93701 


.200000 


n 


n 2 


Vn 


Vio™ 


n* 


-\fn 


JllOn 


fllOOn 


1/n 



102 




Powers — 


Roots - 


- Reciprocals 




[VI 


n 


n 2 


Vn 




n 3 


^n 






1/n 


VlOn 


VlOn 


VlOOn 


5.00 


25.0000 


2.23607 


7.07107 


125.000 


1.70998 


3.68403 


7.93701 


.200000 


5.01 
5.02 
5.03 

5.04 
5.05 
5.06 

5.07 
5.08 
5.09 


25.1001 
25.2004 
25.3009 

25.4016 
25.5025 
25.6036 

25.7049 
25.8064 
25.9081 


2.23830 
2.24054 

2.24277 

2.24499 

2.24722 
2.24944 

2.25167 
2.25389 
2.25610 


7.07814 
7.08520 
7.09225 

7.09930 
7.10634 
7.11337 

7.12039 
7.12741 
7.13442 


125.752 
126.506 
127.264 

128.024 
128.788 
129.554 

130.324 
131.097 
131.872 


1.71112 
1.71225 
1.71339 

1.71452 
1.71566 
1.71679 

1.71792 
1.71905 
1.72017 


3.68649 
3.68894 
3.69138 

3.69383 
3.69627 
3.69871 

3.70114 
3.70357 
3.70600 


7.94229 
7.94757 
7.95285 

7.95811 
7.96337 
7.96863 

7.97387 
7.97911 
7.98434 


.199601 
.199203 

.198807 

.198413 
.198020 
.197628 

.197239 
.196850 
.196464 


5.10 


26.0100 


2.25832 


7.14143 


132.651 


1.72130 


3.70843 


7.98957 


.196078 


5.11 
5.12 
5.13 

5.14 
5.15 
5.16 

5.17 
5.18 
5.19 


26.1121 
26.2144 
26.3169 

26.4196 
26.5225 
26.6256 

26.7289 
26.8324 
26.9361 


2.26053 
2.26274 
2.26495 

2.26716 
2.26936 
2.27156 

2.27376 
2.27596 
2.27816 


7.14843 
7.15542 
7.16240 

7.16938 
7.17635 
7.18331 

7.19027 
7.19722 
7.20417 


133.433 
134.218 
135.006 

135.797 
136.591 
137.388 

138.188 
138.992 
139.798 


1.72242 
1.72355 
1.72467 

1.72579 
1.72691 
1.72802 

1.72914 
1.73025 
1.73137 


3.71085 
3.71327 
3.71569 

3.71810 
3.72051 
3.72292 

3.72532 
3.72772 
3.73012 


7.99479 
8.00000 
8.00520 

8.01040 
8.01559 
8.02078 

8.02596 
8.03113 
8.03629 


.195695 
.195312 
.194932 

.194553 
.194175 
.193798 

.193424 
.193050 
.192678 


5.20 


27.0400 


2.28035 


7.21110 


140.608 


1.73248 


3.73251 


8.04145 


.192308 


5.21 
5.22 
5.23 

5.24 
5.25 
5.26 

5.27 

5.28 
5.29 


27.1441 
27.2484 
27.3529 

27.4576 
27.5625 
27.6676 

27.7729 

27.8784 
27.9841 


2.28254 

2.28473 
2.28692 

2.28910 
2.29129 
2.29347 

2.29565 

2.29783 
2.30000 


7.21803 
7.22496 
7.23187 

7.23878 
7.24569 
7.25259 

7.25948 
7.26636 
7.27324 


141.421 
142.237 
143.056 

143.878 
144.703 
145.532 

146.363 
147.198 
148.036 


1.73359 
1.73470 
1.73580 

1.73691 
1.73801 
1.73912 

1.74022 
1.74132 
1.74242 


3.73490 
3.73729 
3.73968 

3.74206 
3.74443 
3.74681 

3.74918 
3.75155 
3.75392 


8.04660 
8.05175 
8.05689 

8.06202 
8.06714 
8.07226 

8.07737 
8.08248 
8.08758 


.191939 
.191571 
.191205 

.190840 
.190476 
.190114 

.189753 
.189394 
.189036 


5.30 


28.0900 


2.30217 


7.28011 


148.877 


1.74351 


3.75629 


8.09267 


.188679 


5.31 
5.32 
5.33 

5.34 
5.35 
5.36 

5.37 
5.38 
5.39 


28.1961 
28.3024 
28.4089 

28.5156 
28.6225 
28.7296 

28.8369 
28.9444 
29.0521 


2.30434 
2.30651 
2.30868 

2.31084 
2.31301 
2.31517 

2.31733 
2.31948 
2.32164 


7.28697 
7.29383 
7.30068 

7.30753 
7.31437 
7.32120 

7.32803 
7.33485 
7.34166 


149.721 
150.569 
151.419 

152.273 
153.130 
153.991 

154.854 
155.721 
156.591 


1.74461 
1.74570 
1.74680 

1.74789 
1.74898 
1.75007 

1.75116 
1.75224 
1.75333 


3.75865 
3.76101 
3.76336 

3.76571 
3.76806 
3.77041 

3.77275 

3.77509 
3.77743 


8.09776 
8.10284 
8.10791 

8.11298 
8.11804 
8.12310 

8.12814 
8.13319 

8.13822 


.188324 
.187970 
.187617 

.187266 
.186916 
.186567 

.186220 

.185874 
.185529 


5.40 


29.1600 


2.32379 


7.34847 


157.464 


1.75441 


3.77976 


8.14325 


.185185 


5.41 
5.42 
5.43 

5.44 
5.45 
5.46 

5.47 
5.48 
5.49 


29.2681 
29.3764 
29.4849 

29.5936 
29.7025 
29.8116 

29.9209 
30.0304 
30.1401 


2.32594 
2.32809 
2.33024 

2.33238 
2.33452 
2.33666 

2.33880 
2.34094 
2.34307 


7.35527 
7.36206 
7.36885 

7.37564 
7.38241 
7.38918 

7.39594 
7.40270 
7.40945 


158.340 
159.220 
160.103 

160.989 

161.879' 

162.771 

163.667 
164.567 
165.469 


1.75549 
1.75657 
1.75765 

1.75873 

1.75981 
1.76088 

1.76196 
1.76303 
1.76410 


3.78209 
3.78442 
3.78675 

3.78907 
3.79139 
3.79371 

3.79603 
3.79834 
3.80065 


8.14828 
8.15329 
8.15831 

8.16331 
8.16831 
8.17330 

8.17829 

8.18327 
8.18824 


.184843 
.184502 
.184162 

.183824 
.183486 
.183150 

.182815 
.182482 
.182149 


5.50 


30.2500 


2.34521 


7.41620 


166.375 


1.76517 


3.80295 


8.19321 


.181818 


n 


n 2 


V^ 


VlOn 


n 3 


Vn" 


VlOn 


VlOOn 


1/n 



VI] 




Powers — 


Roots - 


— Reciprocals 




103 


n 


n 2 


Vn 




n 3 








1/n 


VlOn 


$n 


illOn 


^100 n 


5.50 


30.2500 


2.34521 


7.41620 


166.375 


1.76517 


3.80295 


8.19321 


.181818 


5.51 
5.52 
5.53 

5.54 
5.55 
5.56 

5.57 
5.58 
5.59 


30.3601 
30.4704 
30.5809 

30.6916 
30.8025 
30.9136 

31.0249 
31.1364 
31.2481 


2.34734 
2.34947 
2.35160 

2.35372 
2.35584 
2.35797 

2.36008 
2.36220 
2.36432 


7.42294 
7.42967 
7.43640 

7.44312 
7.44983 
7.45654 

7.46324 
7.46994 
7.47663 


167.284 
168.197 
169.112 

170.031 
170.954 
171.880 

172.809 
173.741 
174.677 


1.76624 
1.76731 
1.76838 

1.76944 
1.77051 
1.77157 

1.77263 
1.77369 
1.77475 


3.80526 
3.80756 
3.80985 

3.81215 
3.81444 
3.81673 

3.81902 
3.82130 
3.82358 


8.19818 
8.20313 
8.20808 

8.21303 

8.21797 
8.22290 

8.22783 
8.23275 
8.23766 


.181488 
.181159 
.180832 

.180505 
.180180 
.179856 

.179533 
.179211 
.178891 


5.60 


31.3600 


2.36643 


7.48331 


175.616 


1.77581 


3.82586 


8.24257 


.178571 


5.61 
5.62 
5.63 

5.64 
5.65 
5.66 

5.67 
5.68 
5.69 


31.4721 
31.5844 
31.6969 

31.8096 
31.9225 
32.0356 

32.1489 
32.2624 
32.3761 


2.36854 
2.37065 
2.37276 

2.37487 
2.37697 
2.37908 

2.38118 
2.38328 
2.38537 


7.48999 
7.49667 
7.50333 

7.50999 
7.51665 
7.52330 

7.52994 
7.53658 
7.54321 


176.558 
177.504 
178.454 

179.406 
180.362 
181.321 

182.284 
183.250 
184.220 


1.77686 
1.77792 

1.77897 

1.78003 
1.78108 
1.78213 

1.78318 

1.78422 
1.78527 


3.82814 
3.83041 
3.83268 

3.83495 
3.83722 
3.83948 

3.84174 
3.^4399 
3.84625 


8.24747 
8.25237 
8.25726 

8.26215 
8.26703 
8.27190 

8.27677 
8.28164 
8.28649 


.178253 
.177936 
.177620 

.177305 
.176991 
.176678 

.176367 
.176056 
.175747 


5.70 


32.4900 


2.38747 


7.54983 


185.193 


1.78632 


3.84850 


8.29134 


.175439 


5.71 
5.72 
5.73 

5.74 
5.75 
5.76 

5.77 
5.78 
5.79 


32.6041 
32.7184 
32.8329 

32.9476 
33.0625 
33.1776 

33.2929 
33.4084 
33.5241 


2.38956 
2.39165 
2.39374 

2.39583 
2.39792 
2.40000 

2.40208 
2.40416 
2.40624 


7.55645 
7.56307 
7.56968 

7.57628 
7.58288 
7.58947 

7.59605 
7.60263 
7.60920 


186.169 
187.149 
188.133 

189.119 
190.109 
191.103 

192.100 
193.101 
194.105 


1.78736 
1.78840 
1.78944 

1.79048 
1.79152 
1.79256 

1.79360 
1.79463 
1.79567 


3.85075 
3.85300 
3.85524 

3.85748 
3.85972 
3.86196 

3.86419 
3.86642 
3.86865 


8.29619 
8.30103 
8.30587 

8.31069 
8.31552 
8.32034 

8.32515 
8.32995 
8.33476 


.175131 
.174825 
.174520 

.174216 
.173913 
.173611 

.173310 
.173010 
.172712 


5.80 


33.6400 


2.40832 


7.61577 


195.112 


1.79670 


3.87088 


8.33955 


.172414 


5.81 
5.82 
5.83 

5.84 

5.85 
5.86 

5.87 
5.88 
5.89 


33.7561 
33.8724 
33.9889 

34.1056 
34.2225 
34.3396 

34.4569 
34.5744 
34.6921 


2.41039 
2.41247 
2.41454 

2.41661 
2.41868 
2.42074 

2.42281 
2.42487 
2.42693 


7.62234 
7.62889 
7.63544 

7.64199 
7.64853 
7.65506 

7.66159 
7.66812 
7.67463 


196.123 
197.137 
198.155 

199.177 
200.202 
201.230 

202.262 
203.297 
204.336 


1.79773 
1.79876 
1.79979 

1.80082 
1.80185 

1.80288 

1.80390 
1.80492 
1.80595 


3.87310 
3.87532 
3.87754 

3.87975 
3.88197 

3.88418 

3.88639 

3.88859 
3.89080 


8.34434 
8.34913 
8.35390 

8.35868 
8.36345 
8.36821 

8.37297 

8.37772 
8.38247 


.172117 
.171821 
.171527 

.171233 
.170940 
.170649 

.170358 

.170068 
.169779 


5.90 


34.8100 


2.42899 


7.68115 


205.379 


1.80697 


3.89300 


8.38721 


.169492 


5.91 
5.92 
5.93 

5.94 
5.95 
5.96 

5.97 
5.98 
5.99 


34.9281 
35.0464 
35.1649 

35.2836 
35.4025 
35.5216 

35.6409 
35.7604 

35.8801 


2.43105 
2.43311 
2.43516 

2.43721 
2.43926 
2.44131 

2.44336 
2.44540 
2.44745 


7.68765 
7.69415 
7.70065 

7.70714 
7.71362 
7.72010 

7.72658 
7.73305 
7.73951 


206.425 
207.475 
208.528 

209.585 
210.645 
211.709 

212.776 
213.847 
214.922 


1.80799 
1.80901 
1.81003 

1.81104 
1.81206 
1.81307 

1.81409 
1.81510 
1.81611 


3.89519 
3.89739 
3.89958 

3.90177 
3.90396 
3.90615 

3.90833 
3.91051 
3.91269 


8.39194 
8.39667 
8.40140 

8.40612 
8.41083 
8.41554 

8.42025 
8.42494 
8.42964 


.169205 
.168919 
.168634 

.168350 
.168067 
.167785 

.167504 
.167224 
.166945 


6.00 


36.0000 


2.44949 


7.74597 


216.000 


1.81712 


3.91487 


8.43433 


.166667 


n 


n 2 


V^ 


VlOn 


n 3 


$n 


yllOn 


<ll00n 


1/n 



104 




Powers — 


Roots - 


— Reciprocals 




[VI 


n 


n 2 


-fn 


VlOn 


n 3 


^n 


^10 n 


VlOOn 


1/n 


6.00 


36.0000 


2.44949 


7.74597 


216.000 


1.81712 


3.91487 


8.43433 


.166667 


6.01 
6.02 
6.03 

6.04 
6.05 
6.06 

6.07 
6.08 
6.09 


36.1201 
36.2404 
36.3609 

36.4816 
36.6025 
36.7236 

36.8449 
36.9664 
37.0881 


2.45153 
2.45357 
2.45561 

2.45764 
2.45967 
2.46171 

2.46374 

2.46577 
2.46779 


7.75242 
7.75887 
7.76531 

7.77174 
7.77817 
7.78460 

7.79102 
7.79744 
7.80385 


217.082 
218.167 
219.256 

220.349 
221.445 
222.545 

223.649 
224.756 

225.867 


1.81813 
1.81914 
1.82014 

1.82115 
1.82215 
1.82316 

1.82416 
1.82516 
1.82616 


3.91704 
3.91921 
3.92138 

3.92355 
3.92571 
3.92787 

3.93003 
3.93219 
3.93434 


8.43901 
8.44369 
8.44836 

8.45303 
8.45769 
8.46235 

8.46700 
8.47165 
8.47629 


.166389 
.166113 
.165837 

.165563 
.165289 
.165017 

.164745 
.164474 
.164204 


6.10 


37.2100 


2.46982 


7.81025 


226.981 


1.82716 


3.93650 


8.48093 


.163934 


6.11 
6.12 
6.13 

6.14 
6.15 
6.16 

6.17 
6.18 
6.19 


37.3321 
37.4544 
37.5769 

37.6996 
37.8225 
37.9456 

38.0689 
38.1924 
38.3161 


2.47184 
2.47386 

2.47588 

2.47790 
2.47992 
2.48193 

2.48395 
2.48596 

2.48797 


7.81665 
7.82304 
7.82943 

7.83582 
7.84219 

7.84857 

7.85493 
7.86130 
7.86766 


228.099 
229.221 
230.346 

231.476 
232.608 
233.745 

234.885 
236.029 
237.177 


1.82816 
1.82915 
1.83015 

1.83115 
1.83214 
1.83313 

1.83412 
1.83511 
1.83610 


3.93865 
3.94079 
3.94294 

3.94508 
3.94722 
3.94936 

3.95150 
3.95363 
3.95576 ' 


8.48556 
8.49018 
8.49481 

8.49942 
8.50403 
8.50864 

8.51324 

8.51784 
8.52243 


.163666 
.163399 
.163132 

.162866 
.162602 
.162338 

.162075 
.161812 
.161551 


6.20 


38.4400 


2.48998 


7.87401 


238.328 


1.83709 


3.95789 


8.52702 


.161290 


6.21 
6.22 
6.23 

6.24 
6.25 
6.26 

6.27 
6.28 
6.29 


38.5641 
38.6884 
38.8129 

38.9376 
39.0625 
39.1876 

39.3129 
39.4384 
39.5641 


2.49199 
2.49399 
2.49600 

2.49800 
2.50000 
2.50200 

2.50400 
2.50599 
2.50799 


7.88036 
7.88670 
7.89303 

7.89937 
7.90569 
7.91202 

7.91833 
7.92465 
7.93095 


239.483 
240.642 

241.804 

242.971 
244.141. 
245.314 

246.492 
247.673 

248.858 


1.83808 
1.83906 
1.84005 

1.84103 
1.84202 
1.84300 

1.84398 
1.84496 
1.84594 


3.96002 
3.96214 
3.96427 

3.96638 
3.96850 
3.97062 

3.97273 
3.97484 
3.97695 


8.53160 
8.53618 
8.54075 

8.54532 

8.54988 
8.55444 

8.55899 
8.56354 
8.56808 


.161031 
.160772 
.160514 

.160256 
.160000 
.159744 

.159490 
.159236 
.158983 


6.30 


39.6900 


2.50998 


7.93725 


250.047 


1.84691 


3.97906 


8.57262 


.158730 


6.31 
6.32 
6.33 

6.34 
6.35 
6.36 

6.37 
6.38 
6.39 


39.8161 
39.9424 
40.0689 

40.1956 
40.3225 
40.4496 

4GT.5769 
40.7044 
40.8321 


2.51197 
2.51396 
2.51595 

2.51794 
2.51992 
2.52190 

2.52389 
2.52587 
2.52784 


7.94355 
7.94984 
7.95613 

7.96241 
7.96869 
7.97496 

7.98123 
7.98749 
7.99375 


251.240 
252.436 
253.636 

254.840 
256.048 
257.259 

258.475 
259.694 
260.917 


1.84789 
1.84887 
1.84984 

1.85082 
1.85179 
1.85276 

1.85373 
1.85470 
1.85567 


3.98116 
3.98326 
3.98536 

3.98746 
3.98956 
3.99165 

3.99374 
3.99583 
3.99792 


8.57715 
8.58168 
8.58620 

8.59072 
8.59524 
8.59975 

8.60425 
8.60875 
8.61325 


.158479 
.158228 
.157978 

.157729 
.157480 
.157233 

.156986 
.156740 
.156495 


6.40 


40.9600 


2.52982 


8.00000 


262.144 


1.85664 


4.00000 


8.61774 


.156250 


6.41 
6.42 
6.43 

6.44 
6.45 
6.46 

6.47 
6.48 
6.49 


41.0881 
41.2164 
41.3449 

41.4736 
41.6025 
41.7316 

41.8609 
41.9904 
42.1201 


2.53180 
2.53377 
2.53574 

2.53772 
2.53969 
2.54165 

2.54362 
2.54558 
2.54755 


8.00625 
8.01249 
8.01873 

8.02496 
8.03119 
8.03741 

8.04363 
8.04984 
8.05605 


263.375 
264.609 
265.848 

267.090 
268.336 
269.586 

270.840 
272.098 
273.359 


1.85760 
1.85857 
1.85953 

1.86050 
1.86146 
1.86242 

1.86338 
1.86434 
1.86530 


4.00208 
4.00416 
4.00624 

4.00832 
4.01039 
4.01246 

4.01453 
4.01660 
4.01866 


8.62222 
8.62671 
8.63118 

8.63566 
8.64012 
8.64459 

8.64904 
8.65350 
8.65795 


.156006 
.155763 
.155521 

.155280 
.155039 
.154799 

.154560 
.154321 
.154083 


6.50 


42.2500 


2.54951 


8.06226 


274.625 


1.86626 


4.02073 


8.66239 


.153846 


n 


n 2 


Vn 


VlOn 


n 3 


-fin 


HlOn 


^100 n 


1/n 



VI] 




Powers — 


Roots - 


— Reciprocals 




105 


n 


n 2 


V™ 




n 3 


-\ln 






l/n 


VlOn 


^10 n 


JllOOn 


6.50 


42.2500 


2.54951 


8.06226 


274.625 


1.86626 


4.02073 


8.66239 


.153846 


6.51 
6.52 
6.53 

6.54 
6.55 
6.56 

6.57 
6.58 
6.59 


42.3801 
42.5104 
42.6409 

42.7716 
42.9025 
43.0336 

43.1649 
43.2964 
43.4281 


2.55147 
2.55343 
2.55539 

2.55734 
2.55930 
2.56125 

2.56320 
2.56515 
2.56710 


8.06846 
8.07465 
8.08084 

8.08703 
8.09321 
8.09938 

8.10555 
8.11172 

8.11788 


275.894 
277.168 
278.445 

279.726 
281.011 
282.300 

283.593 
284.890 
286.191 


1.86721 
1.86817 
1.86912 

1.87008 
1.87103 
1.87198 

1.87293 

1.87388 
1.87483 


4.02279 
4.02485 
4.02690 

4.02896 
4.03101 
4.03306 

4.03511 
4.03715 
4.03920 


8.66683 
8.67127 
8.67570 

8.68012 
8.68455 
8.68896 

8.69338 
8.69778 
8.70219 


.153610 
.153374 
.153139 

.152905 
.152672 
.152439 

.152207 
.151976 
.151745 


6.60 


43.5600 


2.56905 


8.12404 


287.496 


1.87578 


4.04124 


8.70659 


.151515 


6.61 
6.62 
6.63 

6.64 
6.65 
6.66 

6.67 
6.68 
6.69 


43.6921 
43.8244 
43.9569 

44.0896 
44.2225 
44.3556 

44.4889 
44.6224 
44.7561 


2.57099 
2.57294 

2.57488 

2.57682 
2.57876 
2.58070 

2.58263 
2.58457 
2.58650 


8.13019 
8.13634 
8.14248 

8.14862 
8.15475 
8.16088 

8.16701 
8.17313 
8.17924 


288.805 
290.118 
291.434 

292.755 
294.080 
295.408 

296.741 
298.078 
299.418 


1.87672 
1.87767 
1.87862 

1.87956 
1.88050 
1.88144 

1.88239 
1.88333 

1.88427 


4.04328 
4.04532 
4.04735 

4.04939 
4.05142 
4.05345 

4.05548 
4.05750 
4.05953 


8.71098 
8.71537 
8.71976 

8.72414 

8.72852 
8.73289 

8.73726 
8.74162 
8.74598 


.151286 
.151057 
.150830 

.150602 
.150376 
.150150 

.149925 
.149701 
.149477 


6.70 


44.8900 


2.58844 


8.18535 


300.763 


1.88520 


4.06155 


8.75034 


.149254 


6.71 
6.72 
6.73 

6.74 
6.75 
6.76 

6.77 
6.78 
6.79 


45.0241 
45.1584 
45.2929 

45.4276 
45.5625 
45.6976 

45.8329 
45.9684 
46.1041 


2.59037 
2.59230 
2.59422 

2.59615 
2.59808 
2.60000 

2.60192 
2.60384 
2.60576 


8.19146 
8.19756 
8.20366 

8.20975 
8.21584 
8.22192 

8.22800 
8.23408 
8.24015 


302.112 
303.464 
304.821 

306.182 
307.547 
308.916 

310.289 
311.666 
313.047 


1.88614 
1.88708 
1.88801 

1.88895 
1.88988 
1.89081 

1.89175 
1.89268 
1.89361 


4.06357 
4.06559 
4.06760 

4.06961 
4.07163 
4.07364 

4.07564 
4.07765 
4.07965 


8.75469 
8.75904 
8.76338 

8.76772 
8.77205 

8.77638 

8.78071 
8.78503 
8.78935 


.149031 
.148810 
.148588 

.148368 
.148148 
.147929 

.147710 
.147493 
.147275 


6.80 


46.2400 


2.60768 


8.24621 


314.432 


1.89454 


4.08166 


8.79366 


.147059 


6.81 
6.82 
6.83 

6.84 
6.85 
6.86 

6.87 

6.88 
6.89 


46.3761 
46.5124 
46.6489 

46.7856 
46.9225 
47.0596 

47.1969 
47.3344 
47.4721 


2.60960 
2.61151 
2.61343 

2.61534 
2.61725 
2.61916 

2.62107 
2.62298 
2.62488 


8.25227 
8.25833 
8.26438 

8.27043 
8.27647 
8.28251 

8.28855 
8.29458 
8^30060 


315.821 
317.215 
318.612 

320.014 
321.419 
322.829 

324.243 
325.661 
327.083 


1.89546 
1.89639 
1.89732 

1.89824 
1.89917 
1.90009 

1.90102 


4.08365 
4.08565 
4.08765 

4.08964 
4.09163 
4.09362 

4.09561 


8.79797 
8.80227 
8.80657 

8.81087 
8.81516 
8.81945 

8.82373 
8.82801 
8.83228 


.146843 
.146628 
.146413 

.146199 
.145985 
.145773 

.145560 
.145349 
.145138 


1.90194 
1.90286 


4.09760 
4.09958 


6.90 


47.6100 


2.62679 


8.30662 


328.509 


1.90378 


4.10157 


8.83656 


.144928 


6.91 
6.92 
6.93 

6.94 
6.95 
6.96 

6.97 
6.98 
6.99 


47.7481 
47.8864 
48.0249 

48.1636 
48.3025 
48.4416 

48.5809 
48.7204 
48.8601 


2.62869 
2.63059 
2.63249 

2.63439 
2.63629 
2.63818 

2.64008 
2.64197 
2.64386 


8.31264 
8.31865 
8.32466 

8.33067 
8.33667 
8.34266 

8.34865 
8.35464 
8.36062 


329.939 
331.374 
332.813 

334.255 
335.702 
337.154 

338.609 
340.068 
341.532 


1.90470 
1.90562 
1.90653 

1.90745 
1.90837 
1.90928 

1.91019 
1.91111 
1.91202 


4.10355 
4.10552 
4.10750 

4.10948 
4.11145 
4.11342 

4.11539 
4.11736 
4.11932 


8.84082 
8.84509 
8.84934 

8.85360 
8.85785 
8.86210 

8.86634 
8.87058 
8.87481 


.144718 
.144509 
.144300 

.144092 
.143885 
.143678 

.143472 
.143266 
.143062 


7.00 


49.0000 


2.64575 


8.36660 


343.000 


1.91293 


4.12129 


8.87904 


.142857 


n 


n 2 


V^ 


VlOn 


n 3 


<fc 


JllOn 


^100 n\ l/n 



106 




Powers — 


Roots - 


— Reciprocals 




[VI 


n 


n 2 


v^ 


VlOn 


n 3 


-yfn 


^10 n 


ShLOOn 


1/n 


7.00 


49.0000 


2.64575 


8.36660 


343.000 


1.91293 


4.12129 


8.87904 


.142857 


7.01 
7.02 
7.03 

7.04 
7.05 
7.06 

7.07 
7.08 
7.09 


49.1401 
49.2804 
49.4209 

49.5616 
49.7025 
49.8436 

49.9849 
50.1264 
50.2681 


2.64764 
2.64953 
2.65141 

2.65330 
2.65518 
2.65707 

2.65895 
2.66083 
2.66271 


8.37257 
8.37854 
8.38451 

8.39047 
8.39643 
8.40238 

8.40833 
8.41427 
8.42021 


344.472 
345.948 
347.429 

348.914 
350.403 
351.896 

353.393 
354.895 
356.401 


1.91384 
1.91475 
1.91566 

1.91657 
1.91747 
1.91838 

1.91929 
1.92019 
1.92109 


4.12325 
4.12521 
4.12716 

4.12912 
4.13107 
4.13303 

4.13498 
4.13693 

4.13887 


8.88327 
8.88749 
8.89171 

8.89592 
8.90013 
8.90434 

8.90854 
8.91274 
8.91693 


.142653 
.142450 
.142248 

.142045 
.141844 
.141643 

.141443 
.141243 
.141044 


7.10 


50.4100 


2.66458 


8.42615 


357.911 


1.92200 


4.14082 


8.92112 


.140845 


7.11 
7.12 
7.13 

7.14 
7.15 
7.16 

7.17 

7.18 
7.19 


50.5521 
50.6944 
50.8369 

50.9796 
51.1225 
51.2656 

51.4089 
51.5524 
51.6961 


2.66646 
2.66833 
2.67021 

2.67208 
2.67395 
2.67582 

2.67769 
2.67955 

2.68142 


8.43208 
8.43801 
8.44393 

8.44985 
8.45577 
8.46168 

8.46759 
8.47349 
8.47939 


359.425 
360.944 
362.467 

363.994 
365.526 
367.062 

368.602 
370.146 
371.695 


1.92290 
1.92380 
1.92470 

1.92560 
1.92650 
1.92740 

1.92829 
1.92919 
1.93008 


4.14276 
4.14470 
4.14664 

4.14858 
4.15052 
4.15245 

4.15438 
4.15631 
4.15824 


8.92531 
8.92949 
8.93367 

8.93784 
8.94201 
8.94618 

8.95034 
8.95450 
8.95866 


.140647 
.140449 
.140252 

.140056 
.139860 
.139665 

.139470 
.139276 
.139082 


7.20 


51.8400 


2.68328 


8.48528 


373.248 


1.93098 


4.16017 


8.96281 


.138889 


7.21 
7.22 
7.23 

7.24 
7.25 
7.26 

7.27 
7.28 
7.29 


51.9841 
52.1284 

52.2729 

52.4176 
52.5625 
52.7076 

52.8529 
52.9984 
53.1441 


2.68514 

2.68701 

2.68887 

2.69072 
2.69258 
2.69444 

2.69629 
2.69815 
2.70000 


8.49117 
8.49706 
8.50294 

8.50882 
8.51469 
8.52056 

8.52643 
8.53229 
8.53815 


374.805 
376.367 
377.933 

379.503 
381.078 
382.657 

384.241 

385.828 
387.420 


1.93187 
1.93277 
1.93366 

1.93455 
1.93544 
1.93633 

1.93722 
1.93810 
1.93899 


4.16209 
4.16402 
4.16594 

4.16786 
4.16978 
4.17169 

4.17361 
4.17552 
4.17743 


8.96696 
8.97110 
8.97524 

8.97938 
8.98351 
8.98764 

8.99176 
8.99588 
9.00000 


.138696 
.138504 
.138313 

.138122 
.137931 
.137741 

.137552 
.137363 
.137174 


7.30 


53.2900 


2.70185 


8.54400 


389.017 


1.93988 


4.17934 


9.00411 


.136986 


7.31 
7.32 
7.33 

7.34 
7.35 
7.36 

7.37 

7.38 
7.39 


53.4361 
53.5824 
53.7289 

53.8756 
54.0225 
54.1696 

54.3169 
54.4644 
54.6121 


2.70370 
2.70555 
2.70740 

2.70924 
2.71109 
2.71293 

2.71477 
2.71662 
2.71846 


8.54985 
8.55570 
8.56154 

8.56738 
8.57321 
8.57904 

8.58487 
8.59069 
8.59651 


390.618 
392.223 
393.833 

395.447 
397.065 
398.688 

400.316 
401.947 
403.583 


1.94076 
1.94165 
1.94253 

1.94341 
1.94430 
1.94518 

1.94606 
1.94694 
1.94782 


4.18125 
4.18315 
4.18506 

4.18696 
4.18886 
4.19076 

4.19266 
4.19455 
4.19644 


9.00822 
9.01233 
9.01643 

9.02053 
9.02462 
9.02871 

9.03280 
9.03689 
9.04097 


.136799 
.136612 
.136426 

.136240 
.136054 
.135870 

.135685 
.135501 
.135318 


7.40 


54.7600 


2.72029 


8.60233 


405.224 


1.94870 


4.19834 


9.04504 


.135135 


7.41 

7.42 
7.43 

7.44 
7.45 
7.46 

7.47 
7.48 
7.49 


54.9081 
55.0564 
55.2049 

55.3536 
55.5025 
55.6516 

55.8009 
55.9504 
56.1001 


2.72213 
2.72397 
2.72580 

2.72764 
2.72947 
2.73130 

2.73313 
2.73496 
2.73679 


8.60814 
8.61394 
8.61974 

8.62554 
8.63134 
8.63713 

8.64292 
8.64870 
8.65448 


406.869 
408.518 
410.172 

411.831 
413.494 
415.161 

416.833 
418.509 
420.190 


1.94957 
1.95045 
1.95132 

1.95220 
1.95307 
1.95395 

1.95482 
1.95569 
1.95656 


4.20023 
4.20212 
4.20400 

4.20589 
4.20777 
4.20965 

4.21153 
4.21341 
4.21529 


9.04911 
9.05318 
9.05725 

9.06131 
9.06537 
9.06942 

9.07347 
9.07752 
9.08156 


.134953 
.134771 
.134590 

.134409 
.134228 
.134048 

.133869 
.133690 
.133511 


7.50 


56.2500 


2.73861 


8.66025 


421.875 


1.95743 


4.21716 


9.08560 


.133333 


n 


n 2 


Vra 


VlOn 


n 3 


^ 


^10 n 


<ll00n 


l/n 



VI] 




Powers — 


Roots - 


— Reciprocals 




107 


n 


n 2 


v^ 


VlOrt 


n 3 


^ 


^10 n 


y/lOOn 


1/n 


7.50 


56.2500 


2.73861 


8.66025 


421.875 


1.95743 


4.21716 


9.08560 


.133333 


7.51 
7.52 
7.53 

7.54 
7.55 
7.56 

7.57 

7.58 
7.59 


56.4001 
56.5504 
56.7009 

56.8516 
57.0025 
57.1536 

57.3049 
57.4564 
57.6081 


2.74044 
2.74226 
2.74408 

2.74591 
2.74773 
2.74955 

2.75136 
2.75318 
2.75500 


8.66603 
8.67179 
8.67756 

8.68332 
8.68907 
8.69483 

8.70057 
8.70632 
8.71206 


423.565 
425.259 
426.958 

428.661 
430.369 
432.081 

433.798 
435.520 
437.245 


1.95830 
1.95917 
1.96004 

1.96091 
1.96177 
1.96264 

1.96350 
1.96437 
1.96523 


4.21904 
4.22091 
4.22278 

4.22465 
4.22651 

4.22838 

4.23024 
4.23210 
4.23396 


9.08964 
9.09367 
9.09770 

9.10173 
9.10575 
9.10977 

9.11378 
9.11779 
9.12180 


.133156 
.132979 
.132802 

.132626 
.132450 
.132275 

.132100 
.131926 
.131752 


7.60 


57.7600 


2.75681 


8.71780 


438.976 


1.96610 


4.23582 


9.12581 


.131579 


7.61 
7.62 
7.63 

7.64 
7.65 
7.66 

7.67 
7.68 
7.69 


57.9121 
58.0644 
58.2169 

58.3696 
58.5225 
58.6756 

58.8289 
58.9824 
59.1361 


2.75862 
2.76043 
2.76225 

2.76405 
2.76586 
2.76767 

2.76948 

2.77128 
2.77308 


8.72353 
8.72926 
8.73499 

8.74071 
8.74643 
8.75214 

8.75785 
8.76356 
8.76926 


440.711 
442.451 
444.195 

445.944 
447.697 
449.455 

451.218 
452.985 
454.757 


1.96696 
1.96782 
1.96868 

1.96954 
1.97040 
1.97126 

1.97211 
1.97297 
1.97383 


4.23768 
4.23954 
4.24139 

4.24324 
4.24509 
4.24694 

4.24879 
4.25063 

4.25248 


9.12981 
9.13380 
9.13780 

9.14179 
9.14577 
9.14976 

9.15374 
9.15771 
9.16169 


.131406 
.131234 
.131062 

.130890 
.130719 
.130548 

.130378 
.130208 
.130039 


7.70 


59.2900 


2.77489 


8.77496 


456.533 


1.97468 


4.25432 


9.16566 


.129870 


7.71 
7.72 
7.73 

7.74 
7.75 
7.76 

7.77 
7.78 
7.79 


59.4441 
59.5984 
59.7529 

59.9076 
60.0625 
60.2176 

60.3729 
60.5284 
60.6841 


2.77669 

2.77849 
2.78029 

2.78209 
2.78388 
2.78568 

2.78747 
2.78927 
2.79106 


8.78066 
8.78635 
8.79204 

8.79773 
8.80341 
8.80909 

8.81476 
8.82043 
8.82610 


458.314 
460.100 
461.890 

463.685 
465.484 
467.289 

469.097 
470.911 

472.729 


1.97554 
1.97639 
1.97724 

1.97809 
1.97895 
1.97980 

1.98065 
1.98150 
1.98234 


4.25616 
4.25800 
4.25984 

4.26167 
4.26351 
4.26534 

4.26717 
4.26900 
4.27083 


9.16962 
9.17359 
9.17754 

9.18150 
9.18545 
9.18940 

9.19335 
9.19729 
9.20123 


.129702 
.129534 
.129366 

.129199 
.129032 
.128866 

.128700 
.128535 
.128370 


7.80 


60.8400 


2.79285 


8.83176 


474.552 


1.98319 


4.27266 


9.20516 


.128205 


7.81 
7.82 
7.83 

7.84 
7.85 
7.86 

7.87 
7.88 
7.89 


60.9961 
61.1524 
61.3089 

61.4656 
61.6225 
61.7796 

61.9369 
62.0944 
62.2521 


2.79464 
2.79643 
2.79821 

2.80000 
2.80179 
2.80357 

2.80535 
2.80713 
2.80891 


8.83742 
8.84308 
8.84873 

8.85438 
8.86002 
8.86566 

8.87130 

8.87694 
8.88257 


476.380 
478.212 
480.049 

481.890 
483.737 

485.588 

487.443 
489.304 
491.169 


1.98404 
1.98489 
1.98573 

1.98658 
1.98742 
1.98826 

1.98911 
1.98995 
1.99079 


4.27448 
4.27631 
4.27813 

4.27995 
4.28177 
4.28359 

4.28540 

4.28722 
4.28903 


9.20910 
9.21302 
9.21695 

9.22087 
9.22479 
9.22871 

9.23262 
9.23653 
9.24043 


.128041 
.127877 
.127714 

.127551 
.127389 
.127226 

.127065 
.126904 
.126743 


7.90 


62.4100 


2.81069 


8.88819 


493.039 


1.99163 


4.29084 


9.24434 


.126582 


7.91 
7.92 
7.93 

7.94 
7.95 
7.96 

7.97 
7.98 
7.99 


62.5681 
62.7264 
62.8849 

63.0436 
63.2025 
63.3616 

63.5209 
63.6804 
63.8401 


2.81247 
2.81425 
2.81603 

2.81780 
2.81957 
2.82135 

2.82312 

2.82489 
2.82666 


8.89382 
8.89944 
8.90505 

8.91067 
8.91628 
8.92188 

8.92749 
8.93308 
8.93868 


494.914 
496.793 
498.677 

500.566 
502.460 
504.358 

506.262 
508.170 
510.082 


1.99247 
1.99331 
1.99415 

1.99499 
1.99582 
1.99666 

1.99750 
1.99833 
1.99917 


4.29265 
4.29446 
4.29627 

4.29807 
4.29987 
4.30168 

4.30348 
4.30528 
4.30707 


9.24823 
9.25213 
9.25602 

9.25991 
9.26380 
9.26768 

9.27156 
9.27544 
9.27931 


.126422 
.126263 
.126103 

.125945 
.125786 
.125628 

.125471 
.125313 
.125156 


8.00 


64.0000 


2.82843 


8.94427 


512.000 


2.00000 


4.30887 


9.28318 


.125000 


n 


n 2 


V^ 


VlOn 


n 3 


^ 


illOn 


^100 n 


1/n 



108 




Poi 


arers — 


Roots - 


— Reciprocals 




[VI 


IX 


n 2 


Vri 




n 3 


In 






1/n 


VlOn 


^10 n 


yllOOn 


8.00 


64.0000 


2.82843 


8.94427 


512.000 


2.00000 


4.30887 


9.28318 


.125000 


8.01 
8.02 
8.03 

8.04 
8.05 
8.06 

8.07 
8.08 
8.09 


64.1601 
64.3204 
64.4809 

64.6416 
64.8025 
64.9636 

65.1249 
65.2864 
65.4481 


2.83019 
2.83196 
2.83373 

2.83549 
2.83725 
2.83901 

2.84077 
2.84253 
2.84429 


8.94986 
8.95545 
8.96103 

8.96660 
8.97218 
8.97775 

8.98332 

8.98888 
8.99444 


513.922 
515.850 

517.782 

519.718 
521.660 
523.607. 

525.558 
527.514 
529.475 


2.00083 
2.00167 
2.00250 

2.00333 
2.00416 
2.00499 

2.00582 
2.00664 
2.00747 


4.31066 
4.31246 
4.31425 

4.31604 
4.31783 
4.31961 

4.32140 
4.32318 
4.32497 


9.28704 
9.29091 
9.29477 

9.29862 
9.30248 
9.30633 

9.31018 
9.31402 
9.31786 


.124844 
.124688 
.124533 

.124378 
.124224 
.124069 

.123916 
.123762 
.123609 


8.10 


65.6100 


2.84605 


9.00000 


531.441 


2.00830 


4.32675 


9.32170 


.123457 


8.11 
8.12 
8.13 

8.14 
8.15 
8.16 

8.17 
8.18 
8.19 


65.7721 
65.9344 
66.0969 

66.2596 
66.4225 
66.5856 

66.7489 
66.9124 
67.0761 


2.84781 
2.84956 
2.85132 

2.85307 
2.85482 
2.85657 

2.85832 
2.86007 
2.86182 


9.00555 
9.01110 
9.01665 

9.02219 
9.02774 
9.03327 

9.03881 
9.04434 
9.04986 


533.412 
535.387 
537.368 

539.353 
541.343 
543.338 

545.339 
547.343 
549.353 


2.00912 
2.00995 
2.01078 

2.01160 
2.01242 
2.01325 

2.01407 
2.01489 
2.01571 


4.32853 
4.33031 
4.33208 

4.33386 
4.33563 
4.33741 

4.33918 
4.34095 
4.34271 


9.32553 
9.32936 
9.33319 

9.33702 
9.34084 
9.34466 

9.34847 
9.35229 
9.35610 


.123305 
.123153 
.123001 

.122850 
.122699 
.122549 

.122399 
.122249 
.122100 


&20 


67.2400 


2.86356 


9.05539 


551.368 


2.01653 


4.34448 


9.35990 


.121951 


8.21 

8.22 
8.23 

8.24 
8.25 
8.26 

8.27 
8.28 
8.29 


67.4041 
67.5684 
67.7329 

67.8976 
68.0625 
68.2276 

68.3929 
68.5584 
68.7241 


2.86531 
2.86705 
2.86880 

2.87054 

2.87228 
2.87402 

2.87576 
2.87750 
2.87924 


9.06091 
9.06642 
9.07193 

9.07744 
9.08295 
9.08845 

9.09395 
9.09945 
9.10494 


553.388 
555.412 
557.442 

559.476 
561.516 
563.560 

565.609 
567.664 
569.723 


2.01735 
2.01817 
2.01899 

2.01980 
2.02062 
2.02144 

2.02225 
2.02307 
2.02388 


4.34625 
4.34801 
4.34977 

4.35153 
4.35329 
4.35505 

4.35681 
4.35856 
4.36032 


9.36370 
9.36751 
9.37130 

9.37510 
9.37889 
9.38268 

9.38646 
9.39024 
9.39402 


.121803 
.121655 
.121507 

.121359 
.121212 
.121065 

.120919 
.120773 
.120627 


8.30 


68.8900 


2.88097 


9.11043 


571.787 


2.02469 


4.36207 


9.39780 


.120482 


8.31 
8.32 
8.33 

8.34 
8.35 
8.36 

8.37 
8.38 
8.39 


69.0561 
69.2224 
69.3889 

69.5556 
69.7225 
69.8896 

70.0569 
70.2244 
70.3921 


2.88271 
2.88444 
2.88617 

2.88791 
2.88964 
2.89137 

2.89310 
2.89482 
2.89655 


9.11592 
9.12140 
9.12688 

9.13236 
9.13783 
9.14330 

9.14877 
9.15423 
9.15969 


573.856 
575.930 
578.010 

580.094 
582.183 

584.277 

586.376 

588.480 
590.590 


2.02551 
2.02632 
2.02713 

2.02794 
2.02875 
2.02956 

2.03037 
2.03118 
2.03199 


4.36382 
4.36557 
4.36732 

4.36907 
4.37081 
4.37256 

4.37430 
4.37604 
4.37778 


9.40157 
9.40534 
9.40911 

9.41287 
9.41663 
9.42039 

9.42414 
9.42789 
9.43164 


.120337 
.120192 
.120048 

.119904 
.119760 
.119617 

.119474 
.119332 
.119190 


8.40 


70.5600 


2.89828 


9.16515 


592.704 


2.03279 


4.37952 


9.43539 


.119048 


8.41 

8.42 
8.43 

8.44 
8.45 
8.46 

8.47 
8.48 
8.49 


70.7281 
70.8964 
71.0649 

71.2336 
71.4025 
71.5716 

71.7409 
71.9104 
72.0801 


2.90000 
2.90172 
2.90345 

2.90517 
2.90689 
2.90861 

2.91033 
2.91204 
2.91376 


9.17061 
9.17606 
9.18150 

9.18695 
9.19239 
9.19783 

9.20326 
9.20869 
9.21412 


594.823 
596.948 
599.077 

601.212 
603.351 , 
605.496 

607.645 
609.800 
611.960 


2.03360 
2.03440 
2.03521 

2.03601 
2.03682 
2.03762 

2.03842 
2.03923 
2.04003 


4.38126 
4.38299 
4.38473 

4.38646 
4.38819 
4.38992 

4.39165 
4.39338 
4.39510 


9.43913 
9.44287 
9.44661 

9.45034* 
9.45407 
9.45780 

9.46152 
9.46525 
9.46897 


.118906 
.118765 
.118624 

.118483 
.118343 
.118203 

.118064 
.117925 
.117786 


8.50 


72.2500 


2.91548 


9.21954 


614.125 


2.04083 


4.39683 


9.47268 


.117647 


n 


n 2 


Vn 




n 3 


•yfn 






1/n 


VlOn 


<llOn 


sfaOO n 






VI] 




Powers — 


Roots - 


- Reciprocals 




109 


n 


n 2 


v^ 










1/n 


VlOn 


n 3 


Vn 


ilWn 


VlOOn 


8.50 


72.2500 


2.91548 


9.21954 


614.125 


2.04083 


4.39683 


9.47268 


.117647 


8.51 
8.52 
8.53 

8.54 
8.55 
8.56 

8.57 
8.58 
8.59 


72.4201 
72.5904 
72.7609 

72.9316 
73.1025 
73.2736 

73.4449 
73.6164 

73.7881 


2.91719 
2.91890 
2.92062 

2.92233 

2.92404 
2.92575 

2.92746 
2.92916 
2.93087 


9.22497 
9.23038 
9.23580 

9.24121 
9.24662 
9.25203 

9.25743 
9.26283 
9.26823 


616.295 
618.470 
620.650 

622.836 
625.026 
627.222 

629.423 
631.629 
633.840 


2.04163 
2.04243 
2.04323 

2.04402 

2.04482 
2.04562 

2.04641 
2.04721 
2.04801 


4.39855 
4.40028 
4.40200 

4.40372 
4.40543 
4.40715 

4.40887 
4.41058 
4.41229 


9.47640 
9.48011 
9.48381 

9.48752 
9.49122 
9.49492 

9.49861 
9.50231 
9.50600 


.117509 
.117371 
.117233 

.117096 
.116959 
.116822 

.116686 
.116550 
.116414 


8.60 


73.9600 


2.93258 


9.27362 


636.056 


2.04880 


4.41400 


9.50969 


.116279 


8.61 
8.62 
8.63 

8.64 
8.65 
8.66 

8.67 
8.68 
8.69 


74.1321 
74.3044 

74.4769 

74.6496 
74.8225 
74.9956 

75.1689 
75.3424 
75.5161 


2.93428 
2.93598 
2.93769 

2.93939 
2.94109 
2.94279 

2.94449 
2.94618 
2.94788 


9.27901 
9.28440 

9.28978 

9.29516 
9.30054 
9.30591 

9.31128 
9.31665 
9.32202 


638.277 
640.504 
642.736 

644.973 
647.215 
649.462 

651.714 
653.972 

656.235 


2.04959 
2.05039 
2.05118 

2.05197 
2.05276 
2.05355 

2.05434 
2.05513 
2.05592 


4.41571 
4.41742 
4.41913 

4.42084 
4.42254 
4.42425 

4.42595 
4.42765 
4.42935 


9.51337 
9.51705 
9.52073 

9.52441 

9.52808 
9.53175 

9.53542 
9.53908 
9.54274 


.116144 
.116009 
.115875 

.115741 

.115607 
.115473 

.115340 
.115207 
.115075 


8.70 


75.6900 


2.94958 


9.32738 


658.503 


2.05671 


4.43105 


9.54640 


.114943 


8.71 
8.72 
8.73 

8.74 
8.75 
8.76 

8.77 
8.78 
8.79 


75.8641 
76.0384 
76.2129 

76.3876 
76.5625 
76.7376 

76.9129 

77.0884 
77.2641 


2.95127 
2.95296 
2.95466 

2.95635 
2.95804 
2.95973 

2.96142 
2.96311 
2.96479 


9.33274 
9.33809 
9.34345 

9.34880 
9.35414 
9.35949 

9.36483 
9.37017 
9.37550 


660.776 
663.055 
665.339 

667.628 
669.922 
672.221 

674.526 
676.836 
679.151 


2.05750 
2.05828 
2.05907 

2.05986 
2.06064 
2.06143 

2.06221 
2.06299 
2.06378 


4.43274 
4.43444 
4.43613 

4.43783 
4.43952 
4.44121 

4.44290 
4.44459 
4.44627 


9.55006 
9.55371 
9.55736 

9.56101 
9.56466 
9.56830 

9.57194 
9.57557 
9.57921 


.114811 
.114679 
.114548 

.114416 
.114286 
.114155 

.114025 
.113895 
.113766 


8.80 


77.4400 


2.96648 


9.38083 


681.472 


2.06456 


4.44796 


9.58284 


.113636 


8.81 
8.82 
8.83 

8.84 
8.85 
8.86 

8.87 
8.88 
8.89 


77.6161 
77.7924 
77.9689 

78.1456 
78.3225 
78.4996 

78.6769 

78.8544 
79.0321 


2.96816 
2.96985 
2.97153 

2.97321 

2.97489 
2.97658 

2.97825 
2.97993 
2.98161 


9.38616 
9.39149 
9.39681 

9.40213 
9.40744 
9.41276 

9.41807 
9.42338 
9.42868 


683.798 
686.129 
688.465 

690.807 
693.154 
695.506 

697.864 
700.227 
702.595 


2.06534 
2.06612 
2.06690 

2.06768 
2.06846 
2.06924 


4.44964 
4.45133 
4.45301 

4.45469 
4.45637 
4.45805 


9.58647 
9.59009 
9.59372 

9.59734 
9.60095 
9.60457 

9.60818 
9.61179 
9.61540 


.113507 
.113379 
.113250 

.113122 
.112994 
.112867 

.112740 
.112613 
.112486 


2.07002 
2.07080 
2.07157 


4.45972 
4.46140 
4.46307 


8.90 


79.2100 


2.98329 


9.43398 


704.969 


2.07235 


4.46475 


9.61900 


.112360 


8.91 
8.92 
8.93 

8.94 
8.95 
8.96 

8.97 
8.98 
8.99 


79.3881 
79.5664 
79.7449 

79.9236 
80.1025 
80.2816 

80.4609 
80.6404 
80.8201 


2.98496 
2.98664 
2.98831 

2.98998 
2.99166 
2.99333 

2.99500 
2.99666 
2.99833 


9.43928 
9.44458 
9.44987 

9.45516 
9.46044 
9.46573 

9.47101 
9.47629 
9.48156 


707.348 
709.732 
712.122 

714.517 
716.917 
719.323 

721.734 
724.151 
726.573 


2.07313 
2.07390 
2.07468 

2.07545 
2.07622 
2.07700 

2.07777 
2.07854 
2.07931 


4.46642 
4.46809 
4.46976 

4.47142 
4.47309 
4.47476 

4.47642 
4.47808 
4.47974 


9.62260 
9.62620 
9.62980 

9.63339 
9.63698 
9.64057 

9.64415 
9.64774 
9.65132 


.112233 
.112108 
.111982 

.111857 
.111732 
.111607 

.111483 
.111359 
.111235 


9.00 


81.0000 


3.00000 


9.48683 


729.000 


2.08008 


4.48140 


9.65489 


.111111 


n 


n 2 


V^ 




n 3 


yfn 






1/n 


VlOn 


JllOn 


yllOOn 



110 




Powers — 


Roots - 


- Reciprocals 




[VI 


n 


n 2 


Vn 




n 3 


^ 






1/n 


VlOn 


^10 n 


yllOOn 


9.00 


81.0000 


3.00000 


9.48683 


729.000 


2.08008 


4.48140 


9.65489 


.mm 


9.01 
9.02 
9.03 

9.04 
9.05 
9.06 

9.07 
9.08 
9.09 


81.1801 
81.3604 
81.5409 

81.7216 
81.9025 
82.0836 

82.2649 
82.4464 
82.6281 


3.00167 
3.00333 
3.00500 

3.00666 
3.00832 
3.00998 

3.01164 
3.01330 
3.01496 


9.49210 
9.49737 
9.50263 

9.50789 
9.51315 
9.51840 

9.52365 
9.52890 
9.53415 


731.433 
733.871 
736.314 

738.763 
741.218 
743.677 

746.143 
748.613 
751.089 


2.08085 
2.08162 
2.08239 

2.08316 
2.08393 
2.08470 

2.08546 
2.08623 
2.08699 


4.48306 
4.48472 
4.48638 

4.48803 
4.48969 
4.49134 

4.49299 
4.49464 
4.49629 


9.65847 
9.66204 
9.66561 

9.66918 
9.67274 
9.67630 

9.67986 
9.68342 
9.68697 


.110988 
.110865 
.110742 

.110619 
.110497 
.110375 

.110254 
.110132 
.110011 


9.10 


82.8100 


3.01662 


9.53939 


753.571 


2.08776 


4.49794 


9.69052 


.109890 


9.11 
9.12 
9.13 

9.14 
9.15 
9.16 

9.17 
9.18 
9.19 


82.9921 
83.1744 
83.3569 

83.5396 
83.7225 
83.9056 

84.0889 
84.2724 
84.4561 


3.01828 
3.01993 
3.02159 

3.02324 
3.02490 
3.02655 

3.02820 
3.02985 
3.03150 


9.54463 
9.54987 
9.55510 

9.56033 
9.56556 
9.57079 

9.57601 
9.58123 
9.58645 


756.058 
758.551 
761.048 

763.552 
766.061 
768.575 

771.095 
773.621 
776.152 


2.08852 
2.08929 
2.09005 

2.09081 
2.09158 
2.09234 

2.09310 
2.09386 
2.09462 


4.49959 
4.50123 

4.50288 

4.50452 
4.50616 
4.50781 

4.50945 
4.51108 
4.51272 


9.69407 
9.69762 
9.70116 

9.70470 
9.70824 
9.71177 

9.71531 

9.71884 
9.72236 


.109769 
.109649 
.109529 

.109409 
.109290 
.109170 

.109051 
.108932 
.108814 


9.20 


84.6400 


3.03315 


9.59166 


778.688 


2.09538 


4.51436 


9.72589 


.108696 


9.21 
9.22 
9.23 

9.24 
9.25 
9.26 

9.27 
9.28 
9.29 


84.8241 
85.0084 
85.1929 

85.3776 
85.5625 
85.7476 

85.9329 
86.1184 
86.3041 


3.03480 
3.03645 
3.03809 

3.03974 
3.04138 
3.04302 

3.04467 
3.04631 
3.04795 


9.59687 
9.60208 
9.60729 

9.61249 
9.61769 
9.62289 

9.62808 
9.63328 
9.63846 


781.230 
783.777 
786.330 

788.889 
791.453 
794.023 

796.598 
799.179 
801.765 


2.09614 
2.09690 
2.09765 

2.09841 
2.09917 
2.09992 

2.10068 
2.10144 
2.10219 


4.51599 
4.51763 
4.51926 

4.52089 
4.52252 
4.52415 

4.52578 
4.52740 
4.52903 


9.72941 
9.73293 
9.73645 

9.73996 
9.74348 
9.74699 

9.75049 
9.75400 
9.75750 


.108578 
.108460 
.108342 

.108225 
.108108 
.107991 

.107875 
.107759 
.107643 


9.30 


86.4900 


3.04959 


9.64365 


804.357 


2.10294 


4.53065 


9.76100 


.107527 


9.31 
9.32 
9.33 

9.34 
9.35 
9.36 

9.37 
9.38 
9.39 


86.6761 
86.8624 
87.0489 

87.2356 

87.4225 
87.6096 

87.7969 
87.9844 
88.1721 


3.05123 
3.05287 
3.05450 

3.05614 
3.05778 
3.05941 

3.06105 
3.06268 
3.06431 


9.64883 
9.65401 
9.65919 

9.66437 
9.66954 
9.67471 

9.67988 
9.68504 
9.69020 


806.954 
809.558 
812.166 

814.781 
817.400 
820.026 

822.657 
825.294 
827.936 


2.10370 
2.10445 
2.10520 

2.10595 
2.10671 
2.10746 

2.10821 
2.10896 
2.10971 


4.53228 
4.53390 
4.53552 

4.53714 
4.53876 
4.54038 

4.54199 
4.54361 
4.54522 


9.76450 
9.76799 
9.77148 

9.77497 
9.77846 
9.78195 

9.78543 
9.78891 
9.79239 


.107411 
.107296 
.107181 

.107066 
.106952 
.106838 

.106724 
.106610 
.106496 


9.40 


88.3600 


3.06594 


9.69536 


830.584 


2.11045 


4.54684 


9.79586 


.106383 


9.41 
9.42 
9.43 

9.44 
9.45 
9.46 

9.47 
9.48 
9.49 


88.5481 
88.7364 
88.9249 

89.1136 
89.3025 
89.4916 

89.6809 
89.8704 
90.0601 


3.06757 
3.06920 
3.07083 

3.07246 
3.07409 
3.07571 

3.07734 
3.07896 
3.08058 


9.70052 
9.70567 
9.71082 

9.71597 
9.72111 
9.72625 

9.73139 
9.73653 
9.74166 


833.238 
835.897 
838.562 

841.232 
843.909 
846.591 

849.278 
851.971 
854.670 


2.11120 
2.11195 
2.11270 

2.11344 
2.11419 
2.11494 

2.11568 
2.11642 
2.11717 


4.54845 
4.55006 
4.55167 

4.55328 

4.55488 
4.55649 

4.55809 
4.55970 
4.56130 


9.79933 
9.80280 
9.80627 

9.80974 
9.81320 
9.81666 

9.82012 
9.82357 
9.82703 


.106270 
.106157 
.106045 

.105932 
.105820 
.105708 

.105597 
.105485 
.105374 


9.50 


90.2500 


3.08221 


9.74679 


857.375 


2.11791 


4.56290 


9.83048 


.105263 


n 


n 2 Vra 


VlOn 


n 3 


-yfn 


^10 n 


^100 n 


1/n 



VI] 




Powers — 


Roots - 


- Reciprocals 




111 


n 


n 2 


Vn 




n 3 








1/n 


VlOn 


Sn 


VlOn 


y/lOOn 


9.50 


90.2500 


3.08221 


9.74679 


857.375 


2.11791 


4.56290 


9.83048 


.105263 


9.51 
9.52 
9.53 

9.54 
9.55 
9.56 

9.57 
9.58 
9.59 


90.4401 
90.6304 
90.8209 

91.0116 
91.2025 
91.3936 

91.5849 
91.7764 
91.9681 


3.08383 
3.08545 
3.08707 

3.08869 
3.09031 
3.09192 

3.09354 
3.09516 
3.09677 


9.75192 
9.75705 
9.76217 

9.76729 
9.77241 
9.77753 

9.78264 

9.78775 
9.79285 


860.085 
862.801 
865.523 

868.251 
870.984 
873.723 

876.467 
879.218 
881.974 


2.11865 
2.11940 
2.12014 

2.12088 
2.12162 
2.12236 

2.12310 
2.12384 
2.12458 


4.56450 
4.56610 
4.56770 

4.56930 
4.57089 
4.57249 

4.57408 
4.57567 
4.57727 


9.83392 
9.83737 
9.84081 

9.84425 
9.84769 
9.85113 

9.85456 
9.85799 
9.86142 


.105152 
.105042 
.104932 

.104822 
.104712 
.104603 

.104493 
.104384 
.104275 


9.60 


92.1600 


3.09839 


9.79796 


884.736 


2.12532 


4.57886 


9.86485 


.104167 


9.61 
9.62 
9.63 

9.64 
9.65 
9.66 

9.67 
9.68 
9.69 


92.3521 
92.5444 
92.7369 

92.9296 
93.1225 
93.3156 

93.5089 
93.7024 
93.8961 


3.10000 
3.10161 
3.10322 

3.10483 
3.10644 
3.10805 

3.10966 
3.11127 
3.11288 


9.80306 
9.80816 
9.81326 

9.81835 
9.82344 
9.82853 

9.83362 
9.83870 
9.84378 


887.504 
890.277 
893.056 

895.841 
898.632 
901.429 

904.231 
907.039 
909.853 


2.12605 
2.12679 
2.12753 

2.12826 

2.12900 
2.12974 

2.13047 
2.13120 
2.13194 


4.58045 
4.58204 
4.58362 

4.58521 
4.58679 
4.58838 

4.58996 
4.59154 
4.59312 


9.86827 
9.87169 
9.87511 

9.87853 
9.88195 
9.88536 

9.88877 
9.89217 
9.89558 


.104058 
.103950 
.103842 

.103734 
.103627 
.103520 

.103413 
.103306 
.103199 


9.70 


94.0900 


3.11448 


9.84886 


912.673 


2.13267 


4.59470 


9.89898 


.103093 


9.71 
9.72 
9.73 

9.74 

9.75 
9.76 

9.77 

9.78 
9.79 


94.2841 
94.4784 
94.6729 

94.8676 
95.0625 
95.2576 

95.4529 
95.6484 
95.8441 


3.11609 
3.11769 
3.11929 

3.12090 
3.12250 
3.12410 

3.12570 
3.12730 
3.12890 


9.85393 
9.85901 
9.86408 

9.86914 
9.87421 
9.87927 

9.88433 
9.88939 
9.89444 


915.499 
918.330 
921.167 

924.010 
926.859 
929.714 

932.575 
935.441 
938.314 


2.13340 
2.13414 
2.13487 

2.13560 
2.13633 
2.13706 

2.13779 
2.13852 
2.13925 


4.59628 
4.59786 
4.59943 

4.60101 
4.60258 
4.60416 

4.60573 
4.60730 
4.60887 


9.90238 
9.90578 
9.90918 

9.91257 
9.91596 
9.91935 

9.92274 
9.92612 
9.92950 


.102987 
.102881 
.102775 

.102669 
.102564 
.102459 

.102354 
.102249 
.102145 


9.80 


96.0400 


3.13050 


9.89949 


941.192 


2.13997 


4.61044 


9.93288 


.102041 


9.81 
9.82 
9.83 

9.84 
9.85 
9.86 

9.87 
9.88 
9.89 


96.2361 
96.4324 
96.6289 

96.8256 
97.0225 
97.2196 

97.4169 
97.6144 
97.8121 


3.13209 
3.13369 
3.13528 

3.13688 
3.13847 
3.14006 

3.14166 
3.14325 
3.14484 


9.90454 
9.90959 
9.91464 

9.91968 
9.92472 
9.92975 

9.93479 
9.93982 
9.94485 


944.076 
946.966 
949.862 

952.764 
955.672 
958.585 

961.505 
964.430 
967.362 


2.14070 
2.14143 
2.14216 

2.14288 
2.14361 
2.14433 

2.14506 
2.14578 
2.14651 


4.61200 
4.61357 
4.61514 

4.61670 
4.61826 
4.61983 

4.62139 
4.62295 
4.62451 


9.93626 
9.93964 
9.94301 

9.94638 
9.94975 
9.95311 

9.95648 
9.95984 
9.96320 


.101937 
.101833 
.101729 

.101626 
.101523 
.101420 

.101317 
.101215 
.101112 


9.90 


98.0100 


3.14643 


9.94987 


970.299 


2.14723 


4.62607 


9.96655 


.101010 


9.91 
9.92 
9.93 

9.94 
9.95 
9.96 

9.97 
9.98 
9.99 


98.2081 
98.4064 
98.6049 

98.8036 
99.0025 
99.2016 

99.4009 
99.6004 
99.8001 


3.14802 
3.14960 
3.15119 

3.15278 
3.15436 
3.15595 

3.15753 
3.15911 
3.16070 


9.95490 
9.95992 
9.96494 

9.96995 
9.97497 
9.97998 

9.98499 
9.98999 
9.99500 


973.242 
976.191 
979.147 

982.108 
985.075 
988.048 

991.027 
994.012 
997.003 


2.14795 
2.14867 
2.14940 

2.15012 
2.15084 
2.15156 

2.15228 
2.15300 
2.15372 


4.62762 
4.62918 
4.63073 

4.63229 
4.63384 
4.63539 

4.63694 
4.63849 
4.64004 


9.96991 
9.97326 
9.97661 

9.97996 
9.98331 
9.98665 

9.98999 
9.99333 
9.99667 


.100908 
.100806 
.100705 

.100604 
.100503 
.100402 

.100301 
.100200 
.100100 


10.00 


100.000 


3.16228 


10.0000 


1000.00 


2.15443 


4.64159 


10.0000 


.100000 


n 


n 2 


V^ 


VlOn| n 3 


Jfo 


^10 n 


^100 n 


1/n 



112 


Table VII 


— Napierian or Natural Logarithms [VII 


N 





1 


2 


3 


4 


5 6 


7 8 9 


0.0 




5.395 


6.088 6.493 


6.781 


7.004 7.187 


7.341 7.474 7.592 


0.1 
0.2 
0.3 


o 7.697 
1 8.391 
g 8.796 


7.793 
8.439 
8.829 


7.880 7.960 
8.486 8.530 
8.861 8.891 


8.034 8.103 8.167 
8.573 8.614 8.653 
8.921 8.950 8.978 


8.228 8.285 8.339 
8.691 8.727 8.762 
9.006 9.032 9.058 


0.4 
0.5 
0.6 


£ 9.084 
U 9.307 
3 9.489 


9.108 9.132 9.156 
9.327 9.346 9.365 
9.506 9.522 9.538 


9.179 9.201 9.223 
9.384 9.402 9.420 
9.554 9.569 9.584 


9.245 9.266 9.287 
9.438 9.455 9.472 
9.600 9.614 9.629 


0.7 
0.8 
0.9 


o 9.643 
H 9.777 

h 9.895 


9.658 9.671 
9.789 9.802 
9.906 9.917 


9.685 
9.814 
9.927 


9.699 9.712 9.726 
9.826 9.837 9.849 
9.938 9.949 9.959 


9.739 9.752 9.764 
9.861 9.872 9.883 
9.970 9.980 9.990 


1.0 


0.00000 


0995 


1980 


2956 


3922 


4879 5827 


6766 7696 8618 


1.1 
1.2 
1.3 


9531 
0.1 8232 
0.2 6236 


*0436 
9062 
7003 


*1333 
9885 
7763 


*2222 
*0701 

8518 


*3103 

*1511 

9267 


*3976 *4842 
*2314 *3111 
*0010 *0748 


*5700 *6551 *7395 
*3902 *4686 *5464 
*1481 *2208 *2930 


1.4 
1.5 
1.6 


0.3 3647 

0.4 0547 

7000 


4359 
1211 
7623 


5066 
1871 
8243 


5767 
2527 

8858 


6464 
3178 
9470 


7156 7844 

3825 4469 

*0078 *0682 


8526 9204 9878 

5108 5742 6373 

*1282 *1879 *2473 


1.7 
1.8 
1.9 


0.5 3063 

8779 

0.6 4185 


3649 
9333 
4710 


4232 
9884 
5233 


4812 

*0432 

5752 


5389 

*0977 

6269 


5962 6531 

*1519 *2058 

6783 7294 


7098 7661 8222 

*2594 *3127 *3658 

7803 8310 8813 


2.0 


9315 


9813 


*0310 


*0804 


*1295 


*1784 *2271 


*2755 *3237 *3716 


2.1 
2.2 
2.3 


0.7 4194 

8846 

0.8 3291 


4669 
9299 
3725 


5142 5612 
9751 *0200 
4157 4587 


6081 

*0648 

5015 


6547 7011 

*1093 *1536 

5442 5866 


7473 7932 8390 

*1978 *2418 *2855 

6289 6710 7129 


2.4 
2.5 
2.6 


7547 

0.9 1629 

5551 


7963 
2028 
6935 


8377 
2426 
6317 


8789 
2822 
6698 


9200 
3216 
7078 


9609 *0016 
3609 4001 
7456 7833 


*0422 *0826 *1228 
4391 4779 5166 
8208 8582 8954 


2.7 
2.8 
2.9 


9325 

1.0 2962 

6471 


9695 
3318 
6815 


*0063 
3674 
7158 


*0430 
4028 
7500 


*0796 
4380 

7841 


*1160 *1523 
4732 5082 
8181 8519 


*1885 *2245 *2604 
5431 5779 6126 
8856 9192 9527 


3.0 


9861 


*0194 


*0526 


*0856 


*1186 


*1514 *1841 


*2168 *2493 *2817 


3.1 
3.2 
3.3 


1.1 3140 
6315 
9392 


3462 
6627 
9695 


3783 4103 
6938 7248 
9996 *0297 


4422 4740 5057 

7557 7865 8173 

*0597 *0896 *1194 


5373 5688 6002 

8479 8784 9089 

*1491 *1788 *2083 


3.4 

3.5 
3.6 


1.2 2378 
5276 
8093 


2671 
5562 
8371 


2964 
5846 
8647 


3256 
6130 
8923 


3547 
6413 
9198 


3837 4127 
6695 6976 
9473 9746 


4415 4703 4990 

7257 7536 7815 

*0019 *0291 *0563 


3.7 
3.8 
3.9 


1.3 0833 
3500 
6098 


1103 
3763 
6354 


1372 
4025 
6609 


1641 
4286 
6864 


1909 
4547 
7118 


2176 2442 
4807 5067 
7372 7624 


2708 2972 3237 
5325 5584 5841 
7877 8128 8379 


4.0 


8629 


8879 


9128 


9377 


9624 


9872 *0118 


*0364 *0610 *0854 


4.1 
4.2 
4.3 


1.4 1099 
3508 
5862 


1342 
3746 
6094 


1585 
3984 
6326 


1828 
4220 
6557 


2070 
4456 

6787 


2311 2552 
4692 4927 
7018 7247 


2792 3031 3270 
5161 5395 5629 
7476 7705 7933 


4.4 

4.5 
4.6 


8160 

1.5 0408 

2606 


8387 
0630 

2823 


8614 
0851 
3039 


8840 
1072 
3256 


9065 
1293 
3471 


9290 9515 
1513 1732 
3687 3902 


9739 9962 *0185 
1951 2170 2388 
4116 4330 4543 


4.7 
4.8 
4.9 


4756 
6862 
8924 


4969 
7070 
9127 


5181 
7277 
9331 


5393 

7485 
9534 


5604 
7691 
9737 


5814 6025 
7898 8104 
9939 *0141 


6235 6444 6653 

8309 8515 8719 

*0342 *0543 *0744 


5.0 


1.6 0944 


1144 


1343 


1542 


1741 


1939 2137 


2334 2531 2728 


N 





1 


2 


3 


4 


5 6 


7 8 9 1 



VII] 



Napierian or Natural Logarithms 



113 



N 





1 


2 


3 


4 


5 


6 


7 


8 9 


5.0 


1.6 0944 


1144 


1343 


1542 


1741 


1939 


2137 


2334 


2531 2728 


5.1 
5.2 
5.3 


2924 
4866 
6771 


3120 
5058 
6959 


3315 
5250 
7147 


3511 
5441 
7335 


3705 
5632 
7523 


3900 
5823 
7710 


4094 
6013 
7896 


4287 
6203 
8083 


4481 4673 
6393 6582 
8269 8455 


5.4 
5.5 
5.6 


8640 
1.7 0475 

2277 


8825 
0656 
2455 


9010 
0838 
2633 


9194 
1019 
2811 


9378 
1199 

2988 


9562 
1380 
3166 


9745 
1560 
3342 


9928 
1740 
3519 


*0111 *0293 
1919 2098 
3695 3871 


5.7 

5.8 
5.9 


4047 
5786 
7495 


4222 
5958 
7665 


4397 
6130 
7834 


4572 
6302 
8002 


4746 
6473 
8171 


4920 
6644 
8339 


5094 

6815 
8507 


5267 
6985 
8675 


5440 5613 
7156 7326 
8842 9009 


6.0 


9176 


9342 


9509 


9675 


9840 *0006 


*0171 


*0336 


*0500 *0665 


6.1 
6.2 
6.3 


1.8 0829 
2455 
4055 


0993 
2616 
4214 


1156 

2777 
4372 


1319 
2938 
4530 


1482 
3098 
4688 


1645 
3258 
4845 


1808 
3418 
5003 


1970 
3578 
5160 


2132 2294 
3737 3895 
5317 5473 


6.4 
6.5 
6.6 


5630 
7180 
8707 


5786 
7334 

8858 


5942 

7487 
9010 


6097 
7641 
9160 


6253 
7794 
9311 


6408 
7947 
9462 


6563 
8099 
9612 


6718 
8251 
9762 


6872 7026 
8403 8555 
9912 *0061 


6.7 

6.8 
6.9 


1.9 0211 
1692 
3152 


0360 
1839 
3297 


0509 
1986 
3442 


0658 
2132 
3586 


0806 
2279 
3730 


0954 
2425 
3874 


1102 
2571 
4018 


1250 
2716 
4162 


1398 1545 
2862 3007 
4305 4448 


7.0 


4591 


4734 


4876 


5019 


5161 


5303 


5445 


5586 


5727 5869 


7.1 

7.2 
7.3 


6009 
7408 

8787 


6150 
7547 
8924 


6291 
7685 
9061 


6431 

7824 
9198 


6571 

7962 
9334 


6711 
8100 
9470 


6851 

8238 
9606 


6991 
8376 

9742 


7130 7269 
8513 8650 
9877 *0013 


7.4 
7.5 
7.6 


2.0 0148 
1490 
2815 


0283 
1624 
2946 


0418 
1757 
3078 


0553 
1890 
3209 


0687 
2022 
33^0 


0821 
2155 
3471 


0956 

2287 
3601 


1089 
2419 
3732 


1223 1357 
2551 2683 
3862 3992 


7.7 
7.8 
7.9 


4122 
5412 
6686 


4252 
5540 
6813 


4381 

5668 
6939 


4511 
5796 
7065 


4640 
5924 
7191 


4769 
6051 
7317 


4898 
6179 
7443 


5027 
6306 
7568 


5156 5284 
6433 6560 
7694 7819 


8.0 


7944 


8069 


8194 


8318 


8443 


8567 


8691 


8815 


8939 9063 


8.1 
8.2 
8.3 


9186 

2.1 0413 

1626 


9310 
0535 
1746 


9433 
0657 
1866 


9556 
0779 
1986 


9679 
0900 
2106 


9802 
1021 
2226 


9924 
1142 
2346 


*0047 *0169 *0291 
1263 1384 1505 
2465 2585 2704 


8.4 
8.5 
8.6 


2823 
4007 
5176 


2942 
4124 
5292 


3061 
4242 
5409 


3180 
4359 
5524 


3298 
4476 
5640 


3417 
4593 
5756 


3535 
4710 
5871 


3653 

4827 
5987 


3771 3889 
4943 5060 
6102 6217 


8.7 
8.8 
8.9 


6332 

7475 
8605 


6447 

%89 
8717 


6562 

7702 
8830 


6677 
7816 
8942 


6791 
7929 
9054 


6905 
8042 
9165 


7020 
8155 
9277 


7134 

8267 
9389 


7248 7361 
8380 8493 
9500 9611 


9.0 


9722 


9834 


9944 *0055 


*0166 *0276 *0387 


*0497 *0607 *0717 


9.1 
9.2 
9.3 


2.2 0827 
1920 
3001 


0937 
2029 
3109 


1047 
2138 
3216 


1157 
2246 
3324 


1266 
2354 
3431 


1375 
2462 
3538 


1485 
2570 
3645 


1594 
2678 
3751 


1703 1812 
2786 2894 
3858 3965 


9.4 
9.5 
9.6 


4071 
5129 
6176 


4177 
5234 
6280 


4284 
5339 
6384 


4390 

5444 
6488 


4496 
5549 
6592 


4601 
5654 
6696 


4707 
5759 
6799 


4813 
5863 
6903 


4918 5024 
5968 6072 
7006 7109 


9.7 

9.8 
9.9 


7213 

8238 
9253 


7316 
8340 
9354 


7419 
8442 
9455 


7521 

8544 
9556 


7624 
8646 
9657 


7727 
8747 
9757 


7829 
8849 
9858 


7932 
8950 
9958 


8034 8136 

9051 9152 

*0058 *0158 


10.0 


2.3 0259 


0358 


0458 


0558 


0658 


0757 


0857 


0956 


1055 1154 


N 





1 


2 


3 


4 


5 


6 


7 


8 9 



114 



Napierian or Natural Logarithms — 10 to 99 



[VII 



10 


2.30259 


25 


3.21888 


40 


3.68888 


55 


4.00733 


70 


4.24850 


85 


4.44265 


11 

12 
13 
14 


2.39790 
2.48491 
2.56495 
2.63906 


26 

27 
28 
29 


3.25810 
3.29584 
3.33220 
3.36730 


41 
42 
43 
44 


3.71357 
3.73767 
3.76120 
3.78419 


56 
57 
58 
59 


4.02535 
4.04305 
4.06044 
4.07754 


71 

72 
73 
74 


4.26268 
4.27667 
4.29046 
4.30407 


86 
87 
88 
89 


4.45435 
4.46591 
4.47734 
4.48864 


15 


2.70805 


30 


3.40120 


45 


3.80666 


60 


4.09434 


75 


4.31749 


90 


4.49981 


16 
17 
18 
19 


2.77259 
2.83321 
2.89037 
2.94444 


31 
32 
33 
34 


3.43399 
3.46574 
3.49651 
3.52636 


46 
47 
48 
49 


3.82864 
3.85015 
3.87120 
3.89182 


61 
62 
63 
64 


4.11087 
4.12713 
4.14313 

4.15888 


76 

77 
78 
79 


4.33073 
4.34381 
4.35671 
4.36945 


91 
92 
93 

94 


4.51086 
4.52179 
4.53260 
4.54329 


20 


2.99573 


35 


3.55535 


50 


3.91202 


65 


4.17439 


80 


4.38203 


95 


4.55388. 


21 
22 
23 
24 


3.04452 
3.09104 
3.13549 
3.17805 


36 
37 
38 
39 


3.58352 
3.61092 
3.63759 
3.66356 


51 
52 
53 
54 


3.93183 
3.95124 
3.97029 
3.98898 


66 
67 
68 
69 


4.18965 
4.20469 
4.21951 
4.23411 


81 
82 
83 
84 


4.39445 
4.40672 
4.41884 
4.43082 


96 
97 
98 
99 


4.56435 
4.57471 
4.58497 
4.59512 





Napierian or Natural Logarithms — 100 to 409 


N 





12 3 


4 5 6 


7 8 9 


10 


4.6 0517 


1512 2497 3473 


4439 5396 6344 


7283 8213 9135 


11 
12 
13 


4.7 0048 
8749 

4.8 6753 


0953 1850 2739 
9579 *0402 *1218 
7520 8280 9035 


3620 4493 5359 

*2028 *2831 *3628 

9784 ♦0527 *1265 


6217 7068 7912 
*4419 *5203 *5981 
*1998 *2725 *3447 


14 
15 
16 


4.9 4164 

5.0 1064 

7517 


4876 5583 6284 
1728 2388 3044 
8140 8760 9375 


6981 7673 8361 
3695 4343 4986 
9987 *0595 *1199 


9043 9721 *0395 

5625 6260 6890 

*1799 *2396 *2990 


17 

18 
19 


5.1 3580 
9296 

5.2 4702 


4166 4749 5329 
9850 *0401 *0949 
5227 5750 6269 


5906 6479 7048 

*1494 *2036 *2575 

6786 7300 7811 


7615 8178 8739 

*3111 *3644 *4175 

8320 8827 9330 


20 


9832 


*0330 *0827 *1321 


*1812 *2301 *2788 


*3272 *3754 *4233 


21 
22 
23 


5.3 4711 
9363 

5.4 3808 


5186 5659 6129 
9816 *0268 *0717 
4242 4674 5104 


6598 7064 7528 

*1165 *1610 *2053 

5532 5959 6383 


7990 8450 8907 

*2495 *2935 *3372 

6806 7227 7646 


24 

25 
26 


8064 

5.5 2146 

6068 


8480 8894 9306 
2545 2943 3339 
6452 6834 7215 


9717 *0126 *0533 
3733 4126 4518 
7595 7973 8350 


*0939 *1343 *1745 
4908 5296 5683 
8725 9099 9471 


27 

28 
29 


9842 

5.6 3479 

6988 


*0212 *0580 *0947 
3835 4191 4545 
7332 7675 8017 


*1313 *1677 *2040 
4897 5249 5599 
8358 8698 9036 


*2402 *2762 *3121 
5948 6296 6643 
9373 9709*0044 


30 


5.7 0378 


0711 1043 1373 


1703 2031 2359 


2685 3010 3334 


31 
32 
33 


3657 
6832 
9909 


3979 4300 4620 

7144 7455 7765 

*0212 *0513 *0814 


4939 5257 5574 

8074 8383 8690 

*1114 *1413 *1711 


5890 6205 6519 

8996 9301 9606 

*2008 *2305 *2600 


34 
35 
36 


5.8 2895 
5793 
8610 


3188 3481 3773 
6079 6363 6647 
8888 9164 9440 


4064 4354 4644 
6930 7212 7493 
9715 9990*0263 


4932 5220 5507 

7774 8053 8332 

*0536 *0808 *1080 


37 
38 
39 


5.9 1350 
4017 
6615 


1620 1889 2158 
4280 4542 4803 
6871 7126 7381 


2426 2693 2959 
5064 5324 5584 
7635 7889 8141 


3225 3489 3754 
5842 6101 6358 
8394 8645 8896 


40 


9146 


9396 9645 9894 


*0141 *0389 *0635 


*0881 *1127 *1372 


N 





12 3 


4 5 6 


7 8 9 



Above 409, use the formula 
or the formula 



log* lOn = log* n -f log* 10 = log* n -f 2.30258509, 
log, n = log« 10-logw n = 2.30258509 logio n. 



VIII] 



Table VIII — Multiples of M and of 1/M 



115 



N 


N-M 


N 


N-M 





0.00000 000 


50 


21.71472 410 


1 
2 
3 

4 
5 
6 

7 
8 
9 

10 


0.43429 448 
0.86858 896 
1.30288 345 

1.73717 793 
2.17147 241 
2.60576 689 

3.04006 137 
3.47435 586 
3.90865 034 


51 
52 
53 

54 
55 
56 

57 

58 
59 


22.14901 858 
22.58331 306 
23.01760 754 

23.45190 202 
23.88619 650 
24.32049 099 

24.75478 547 
25.18907 995 
25.62337 443 


4.34294 482 


60 


26.05766 891 


11 
12 
13 

14 
15 
16 

17 
18 
19 

20 


4.77723 930 
5.21153 378 
5.64582 826 

6.08012 275 
6.51441 723 
6.94871 171 

7.38300 619 
7.81730 067 
8.25159 516 


61 
62 
63 

64 
65 
66 

67 
68 
69 


26.49196 340 
26.92625 788 
27.36055 236 

27.79484 684 
28.22914 132 
28.66343 581 

29.09773 029 
29.53202 477 
29.96631 925 


8.68588 964 


70 


30.40061 373 


21 
22 
23 

24 
25 
26 

27 

28 
29 

30 

31 
32 
33 

34 
35 
36 

37 

38 
39 

40 

41 
42 
43 

44 
45 
46 

47 

48 
49 

50 


9.12018 412 
9.55447 860 
9.98877 308 

10.42306 757 
10.85736 205 
11.29165 653 

11.72595 101 
12.16024 549 
12.59453 998 


71 

72 
73 

74 
75 
76 

77 
78 
79 

80 


30.83490 822 
31.26920 270 
31.70349 718 

32.13779 166 
32.57208 614 
33.00638 062 

33.44067 511 
33.87496 959 
34.30926 407 


13.02883 446 


34.74355 855 


13.46312 894 
13.89742 342 
14.33171 790 

14.76601 238 
15.20030 687 
15.63460 135 

16.06889 583 
16.50319 031 
16.93748 479 


81 
82 
83 

84 
85 
86 

87 
88 
89 


35.17785 303 
35.61214 752 
36.04644 200 

36.48073 648 
36.91503 096 
37.34932 544 

37.78361 993 
38.21791 441 
38.65220 889 


17.37177 928 


90 


39.08650 337 


17.80607 376 
18.24036 824 
18.67466 272 

19.10895 720 
19.54325 169 
19.97754 617 

20.41184 065 
20.84613 513 
21.28042 961 


91 
92 
93 

94 
95 
96 

97 
98 
99 


39.52079 785 
39.95509 234 
40.38938 682 

40.82368 130 
41.25797 578 
41.69227 026 

42.12656 474 
42.56085 923 
42.99515 371 


21.71472 410 


100 


43.42944 819 



2L 



1 

2 
3 

4 
5 
6 

7 
8 
9 

10 

11 
12 
13 

14 
15 
16 

17 
18 
19 

20 

21 
22 
23 

24 
25 
26 

27 
28 
29 

30 

31 
32 
33 

34 
35 
36 

37 

38 
39 


N +M 


N 


N ~M \ 


0.00000 000 


50 


115.12925 465 


2.30258 509 
4.60517 019 
6.90775 528 

9.21034 037 
11.51292 546 
13.81551 056 

16.11809 565 
18.42068 074 
20.72326 584 


51 
52 
53 

54 
55 
56 

57 

58 
59 


117.43183 974 
119.73442 484 
122.03700 993 

124.33959 502 
126.64218 011 
128.94476 521 

131.24735 030 
133.54993 539 
135.85252 049 


23.02585 093 


60 

61 
62 
63 

64 
65 
66 

67 

68 
69 


138.15510 558 


25.32843 602 
27.63102 112 
29.93360 621 

32.23619 130 
34.53877 639 
36.84136 149 

39.14394 658 
41.44653 167 
43.74911 677 


140.45769 067 
142.76027 577 
145.06286 086 

147.36544 595 
149.66803 104 
151.97061 614 

154.27320 123 
156.57578 632 
158.87837 142 


46.05170 186 


70 


161.18095 651 


48.35428 695 
50.65687 205 
52.95945 714 

55.26204 223 
57.56462 732 
59.86721 242 

62.16979 751 
64.47238 260 
66.77496 770 


71 
72 
73 

74 
75 

76 

77 
78 
79 


163.48354 160 
165.78612 670 
168.08871 179 

170.39129 688 
172.69388 197 
174.99646 707 

177.29905 216 
179.60163 725 
181.90422 235 


69.07755 279 


80 


184.20680 744 


71.38013 788 
73.68272 298 
75.98530 807 

78.28789 316 
80.59047 825 
82.89306 335 

85.19564 844 
87.49823 353 
89.80081 863 


81 
82 
83 

84 
85 
86 

87 
88 
89 


186.50939 253 
188.81197 763 
191.11456 272 

193.41714 781 
195.71973 290 
198.02231 800 

200.32490 309 
202.62748 818 
204.93007 328 


40 

41 
42 
43 

44 
45 

46 

47 
48 
49 

50 


92.10340 372 


90 


207.23265 837 


94.40598 881 
96.70857 391 
99.01115 900 

101.31374 409 
103.61632 918 
105.91891 428 

108.22149 937 
110.52408 446 
112.82666 956 


91 
92 
93 

94 
95 
96 

97 

98 
99 


209.53524 346 
211.83782 856 
214.14041 365 

216.44299 874 
218.74558 383 
221.04816 893 

223.35075 402 
225.65333 911- 
227.95592 421 


115.12925 465 


100 


230.25850 930 



M = logio e = .43429 44819 03251 82765 
logio n = log e n • logio e=M log e n. 
logio 6 s =x- logio e =x- Af. 



1/M = log, 10 =2.30258 50929 94045 68402 
log e n = logio n* log e 10 = (l/M) logio n, 

loge (I0 n -Z) = loge X-j-nilJM'L 



116 


Table IX — 


Logarithms of Hyperbolic Functions 


[IX 


X 


Value Logio 


Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


0.00 


1.0000 


.00000 


1.0000 


0.0000 


— oo 


1.0000 


.00000 


.00000 


0.01 
0.02 
0.03 


1.0101 
1.0202 
1.0305 


.00434 
.00869 
.01303 


.99005 
.98020 
.97045 


0.0100 
0.0200 
0.0300 


.00001 
.30106 
.47719 


1.0001 
1.0002 
1.0005 


.00002 
.00009 
.00020 


.01000 
.02000 
.02999- 


0.04 
0.05 
0.06 


1.0408 
1.0513 
1.0618 


.01737 
.02171 
.02606 


.96079 
.95123 
.94176 


0.0400 
0.0500 
0.0600 


.60218 
.69915 
.77841 


1.0008 
1.0013 
1.0018 


.00035 
.00054 
.00078 


.03998 
.04996 
.05993 


0.07 
0.08 
0.09 


1.0725 
1.0833 
1.0942 


.03040 
.03474 
.03909 


.93239 
.92312 
.91393 


0.0701 
0.0801 
0.0901 


.84545 
.90355 
.95483 


1.0025 
1.0032 
1.0041 


.00106 
.00139 
.00176 


.06989 
.07983 
.08976 


0.10 


1.1052 


.04343 


.90484 


0.1002 


.00072 


1.0050 


.00217 


.09967 


0.11 
0.12 
0.13 


1.1163 
1.1275 
1.1388 


.04777 
.05212 
.05646 


.89583 
.88692 
.87810 


0.1102 
0.1203 
0.1304 


.04227 
.08022 
.11517 


1.0061 
1.0072 
1.0085 


.00262 
.00312 
.00366 


.10956 
.11943 
.12927 


0.14 
0.15 
0.16 


1.1503 
1.1618 
1.1735 


.06080 
.06514 
.06949 


.86936 
.86071 
.85214 


0.1405 
0.1506 
0.1607 


.14755 

.17772 
.20597 


1.0098 
1.0113 
1.0128 


.00424 
.00487 
.00554 


.13909 

.14889 
.15865 


0.17 
0.18 
0.19 


1.1853 
1.1972 
1.2092 


.07383 

.07817 
.08252 


.84366 
.83527 
.82696 


0.1708 
0.1810 
0.1911 


.23254 
.25762 
.28136 


1.0145 
1.0162 
1.0181 


.00625 
.00700 
.00779 


.16838 
.17808 

.18775 


0.20 


1.2214 


.08686 


.81873 


0.2013 


.30392. 


1.0201 


.00863 


.19738 


0.21 
0.22 
0.23 


1.2337 
1.2461 
1.2586 


.09120 
.09554 
.09989 


.81058 
.80252 
.79453 


0.2115 
0.2218 
0.2320 


.32541 
.34592 
.36555 


1.0221 
1.0243 
1.0266 


.00951 
.01043 
.01139 


.20697 
.21652 
.22603 


0.24 
0.25 
0.26 


1.2712 

1.2840 
1.2969 


.10423 

.10857 
.11292 


.78663 
.77880 
.77105 


0.2423 
0.2526 
0.2629 


.38437 
.40245 
.41986 


1.0289 
1.0314 
1.0340 


.01239 
.01343 
.01452 


.23550 
.24492 
.25430 


0.27 
0.28 
0.29 


1.3100 
1.3231 
1.3364 


.11726 
.12160 
.12595 


.76338 
.75578 

.74826 


0.2733 
0.2837 
0.2941 


.43663 

.45282 
.46847 


1.0367 
1.0395 
1.0423 


.01564 
.01681 
.01801 


.26362 
.27291 
.28213 


0.30 


1.3499 


.13029 


.74082 


0.3045 


.48362 


1.0453 


.01926 


.29131 


0.31 
0.32 
0.33 


1.3634 
1.3771 
1.3910 


.13463 
.13897 
.14332 


.73345 
.72615 
.71892 


0.3150 
0.3255 
0.3360 


.49830 
.51254 
.52637 


1.0484 
1.0516 
1.0549 


.02054 
.02187 
.02323 


.30044 
.30951 
.31852 


0.34 
0.35 
0.36 


1.4049 
1.4191 
1.4333 


.14766 
.15200 
.15635 


.71177 
.70469 
.69768 


0.3466 
0.3572 
0.3678 


.53981 
.55290 
.56564 


1.0584 
1.0619 
1.0655 


.02463 
.02607 
.02755 


.32748 
.33638 
.34521 


0.37 
0.38 
0.39 


1.4477 
1.4623 
1.4770 


.16069 
.16503 
.16937 


.69073 
.68386 
.67706' 


0.3785 
0.3892 
0.4000 


.57807 
.59019 
.60202 


1.0692 
1.0731 
1.0770 


.02907 
.03063 
.03222 


.35399 
.36271 
.37136 


0.40 


1.4918 


.17372 


.67032 


0.4108 


.61358 


1.0811 


.03385 


.37995 


0.41 
0.42 
0.43 


1.5068 
1.5220 
1.5373 


.17806 
.18240 
.18675 


.66365 
.65705 
.65051 


0.4216 
0.4325 
0.4434 


.62488 
.63594 
.64677 


1.0852 
1.0895 
1.0939 


.03552 
.03723 
.03897 


.38847 
.39693 
.40532 


0.44 
0.45 
0.46 


1.5527 
1.5683 
1.5841 


.19109 
.19543 
.19978 


.64404 
.63763 
.63128 


0.4543 
0.4653 
0.4764 


.65738 

.66777 
.67797 


1.0984 
1.1030 
1.1077 


.04075 
.04256 
.04441 


.41364 
.42190 
.43008 


0.47 
0.48 
0.49 


1.6000 
1.6161 
1.6323 


.20412 
.20846 
.21280 


.62500 
.61878 
.61263 


0.4875 
0.4986 
0.5098 


.68797 
.69779 
.70744 


1.1125 
1.1174 
1.1225 


.04630 

.04822 
.05018 


.43820 
.44624 
.45422 


0.50 


1.6487 


.21715 


.60653 


0.5211 


.71692 


1.1276 


.05217 


.46212 



IX] 


Values and Logarithms of Hyperbolic Functions 


117 


X 


Value Logio 


e~ x 
Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


0.50 


1.6487 


.21715 


.60653 


0.5211 


.71692 


1.1276 


.05217 


.46212 


0.51 
0.52 
0.53 


1.6653 
1.6820 
1.6989 


.22149 

.22583 
.23018 


.60050 
.59452 
.58860 


0.5324 
0.5438 
0.5552 


.72624 
.73540 
.74442 


1.1329 
1.1383 
1.1438 


.05419 
.05625 
.05834 


.46995 
.47770 

.48538 


0.54 
0.55 
0.56 


1.7160 
1.7333 
1.7507 


.23452 

.23886 
.24320 


.58275 
.57695 
.57121 


0.5666 
0.5782 
0.5897 


,75330 
.76204 
.77065 


1.1494 
1.1551 
1.1609 


.06046 
.06262 
.06481 


.49299 
.50052 
.50798 


0.57 
0.58 
0.59 


1.7683 
1.7860 
1.8040 


.24755 
.25189 
.25623 


.56553 
.55990 
.55433 


0.6014 
0.6131 
0.6248 


.77914 
.78751 
.79576 


1.1669 
1.1730 
1.1792 


.06703 
.06929 
.07157 


.51536 
.52267 
.52990 


0.60 


1.8221 


.26058 


.54881 


0.6367 


.80390 


1.1855 


.07389 


.53705 


0.61 
0.62 
0.63 


1.8404 
1.8589 
1.8776 


.26492 
.26926 
.27361 


.54335 
.53794 
.53259 


0.6485 
0.6605 
0.6725 


.81194 
.81987 
.82770 


1.1919 
1.1984 
1.2051 


.07624 
.07861 
.08102 


.54413 
.55113 
.55805 


0.64 
0.65 
0.66 


1.8965 
1.9155 
1.9348 


.27795 

.28229 
.28663 


.52729 
.52205 
.51685 


0.6846 
0.6967 
0.7090 


.83543 
.84308 
.85063 


1.2119 
1.2188 
1.2258 


.08346 
.08593 
.08843 


.56490 
.57167 
.57836 


0.67 
0.68 
0.69 


1.9542 
1.9739 
1.9937 


.29098 
.29532 
.29966 


.51171 

.50662 
.50158 


0.7213 
0.7336 
0.7461 


.85809 
.86548 

.87278 


1.2330 
1.2402 
1.2476 


.09095 
.09351 
.09609 


.58498 
.59152 
.59798 


0.70 


2.0138 


.30401 


.49659 


0.7586 


.88000 


1.2552 


.09870 


.60437 


0.71 
0.72 
0.73 


2.0340 
2.0544 
2.0751 


.30835 
.31269 
.31703 


.49164 
.48675 
.48191 


0.7712 
0.7838 
0.7966 


.88715 
.89423 
.90123 


1.2628 
1.2706 

1.2785 


.10134 
.10401 
.10670 


.61068 
.61691 
.62307 


0.74 
0.75 
0.76 


2.0959 
2.1170 
2.1383 


.32138 
.32572 
.33006 


.47711 
.47237 
.46767 


0.8094 
0.8223 
0.8353 


.90817 
.91504 
.92185 


1.2865 
1.2947 
1.3030 


.10942 
.11216 
.11493 


.62915 
.63515 
.64108 


0.77 
0.78 
0.79 


2.1598 
2.1815 
2.2034 


.33441 
.33875 
.34309 


.46301 
.45841 
.45384 


0.8484 
0.8615 

0.8748 


.92859 
.93527 
.94190 


1.3114 
1.3199 
1.3286 


.11773 
.12055 
.12340 


.64693 
.65271 
.65841 


0.80 


2.2255 


.34744 


.44933 


0.8881 


.94846 


1.3374 


.12627 


.66404 


0.81 
0.82 
0.83 


2.2479 
2.2705 
2.2933 


.35178 
.35612 
.36046 


.44486 
.44043 
.43605 


0.9015 
0.9150 
0.9286 


.95498 
.96144 
.96784 


1.3464 
1.3555 
1.3647 


.12917 
.13209 
.13503 


.66959 
.67507 
.68048 


0.84 
0.85 
0.86 


2.3164 
2.3396 
2.3632 


.36481 
.36915 
.37349 


.43171 

.42741 
.42316 


0.9423 
0.9561 
0.9700 


.97420 
.98051 
.98677 


1.3740 
1.3835 
1.3932 


.13800 
.14099 
.14400 


.68581 
.69107 
.69626 


0.87 
0.88 
0.89 


2.3869 
2.4109 
2.4351 


.37784 
.38218 
.38652 


.41895 
.41478 
.41066 


0.9840 
0.9981 
1.0122 


.99299 
.99916 

.00528 


1.4029 
1.4128 
1.4229 


.14704 
.15009 
.15317 


.70137 
.70642 
.71139 


0.90 


2.4596 


.39087 


.40657 


1.0265 


.01137 


1.4331 


.15627 


.71630 


0.91 
0.92 
0.93 


2.4843 
2.5093 
2.5345 


.39521 
.39955 
.40389 


.40252 
.39852 
.39455 


1.0409 
1.0554 
1.0700 


.01741 
.02341 
.02937 


1.4434 
1.4539 
1.4645 


.15939 
.16254 
.16570 


.72113 
.72590 
.73059 


0.94 
0.95 
0.96 


2.5600 
2.5857 
2.6117 


.40824 
.41258 
.41692 


.39063 
.38674 
.38289 


1.0847 
1.0995 
1.1144 


.03530 
.04119 
.04704 


1.4753 
1.4862 
1.4973 


.16888 
.17208 
.17531 


.73522 

.73978 
.74428 


0.97 
0.98 
0.99 


2.6379 
2.6645 
2,6912 


.42127 
.42561 
.42995 


.37908 
.37531 
.37158 


1.1294 
1.1446 
1.1598 


.05286 
.05864 
.06439 


1.5085 
1.5199 
1.5314 


.17855 
.18181 
.18509 


.74870 
.75307 
.75736 


1.00 


2.7183 


.43429 


.36788 


1.1752 


.07011 


1.5431 


.18839 


.76159 



118 


Values and Logarithms of Hyperbolic Functions 


[IX 


X 


Value Logio 


Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


1.00 


2.7183 


.43429 


.36788 


1.1752 


.07011 


1.5431 


.18839 


.76159 


1.01 

1.02 
1.03 


2.7456 
2.7732 
2.8011 


.43864 
.44298 
.44732 


.36422 
.36060 
.35701 


1.1907 
1.2063 
1.2220 


.07580 
.08146 
.08708 


1.5549 
1.5669 
1.5790 


.19171 
.19504 
.19839 


.76576 
.76987 
.77391 


1.04 
1.05 
1.06 


2.8292 

2.8577 
2.8864 


.45167 
.45601 
.46035 


.35345 
.34994 
.34646 


1.2379 
1.2539 
1.2700 


.09268 
.09825 
.10379 


1.5913 
1.6038 
1.6164 


.20176 
.20515 
.20855 


.77789 
.78181 
.78566 


1.07 
1.08 
1.09 


2.9154 
2.9447 
2.9743 


.46470 
.46904 
.47338 


.34301 

.33960 
.33622 


1.2862 
1.3025 
1.3190 


.10930 
.11479 
.12025 


1.6292 
1.6421 
1.6552 


.21197 
.21541 
.21886 


.78946 
.79320 

.79688 


1.10 


3.0042 


.47772 


.33287 


1.3356 


.12569 


1.6685 


.22233 


.80050 


1.11 
1.12 
1.13 


3.0344 
3.0649 
3.0957 


.48207 
.48641 
.49075 


.32956 
.32628 
.32303 


1.3524 
1.3693 
1.3863 


.13111 
.13649 
.14186 


1.6820 
1.6956 
1.7093 


.22582 
.22931 
.23283 


.80406 
.80757 
.81102 


1.14 
1.15 
1.16 


3.1268 
3.1582 

3.1899 


.49510 
.49944 
.50378 


.31982 

.31664 
.31349 


1.4035 

1.4208 
1.4382 


.14720 
.15253 
.15783 


1.7233 
1.7374 
1.7517 


.23636 
.23990 
.24346 


.81441 
.81775 
.82104 


1.17 

1.18 
1.19 


3.2220 
3.2544 
3.2871 


.50812 
.51247 
.51681 


.31037 
.30728 
.30422 


1.4558 
1.4735 
1.4914 


.16311 
.16836 
.17360 


1.7662 

1.7808 
1.7957 


.24703 
.25062 
.25422 


.82427 
.82745 
.83058 


1.20 


3.3201 


.52115 


.30119 


1.5095 


.17882 


1.8107 


.25784 


.83365 


1.21 
1.22 
1.23 


3.3535 
3.3872 
3.4212 


.52550 
.52984 
.53418 


.29820 
.29523 
.29229 


1.5276 
1.5460 
1.5645 


.18402 
.18920 
.19437 


1.8258 
1.8412 
1.8568 


.26146 
.26510 
.26876 


.83668 
.83965 

.84258 


1.24 
1.25 
1.26 


3.4556 
3.4903 
3.5254 


.53853 

.54287 
.54721 


.28938 
.28650 
.28365 


1.5831 
1.6019 
1.6209 


.19951 
.20464 
.20975 


1.8725 

1.8884 
1.9045 


.27242 
.27610 
.27979 


.84546 

.84828 
.85106 


1.27 
1.28 
1.29 


3.5609 
3.5966 
3.6328 


.55155 
.55590 
.56024 


.28083 
.27804 
.27527 


1.6400 
1.6593 

1.6788 


.21485 
.21993 
.22499 


1.9208 
1.9373 
1.9540 


.28349 
.28721 
.29093 


.85380 
.85648 
.85913 


1.30 


3.6693 


.56458 


.27253 


1.6984 


.23004 


1.9709 


.29467 


.86172 


1.31 
1.32 
1.33 


3.7062 
3.7434 
3.7810 


.56893 
.57327 
.57761 


.26982 
.26714 
.26448 


1.7182 
1.7381 
1.7583 


.23507 
.24009 
.24509 


1.9880 
2.0053 
2.0228 


.29842 
.30217 
.30594 


.86428 
.86678 
.86925 


1.34 
1.35 
1.36 


3.8190 
3.8574 
3.8962 


.58195 
.58630 
.59064 


.26185 
.25924 
.25666 


1.7786 
1.7991 
1.8198 


.25008 
.25505 
.26002 


2.0404 
2.0583 
2.0764 


.30972 
.31352 
.31732 


.87167 
.87405 
.87639 


1.37 
1.38 
1.39 


3.9354 
3.9749 
4.0149 


.59498 
.59933 
.60367 


.25411 
.25158 
.24908 


1.8406 
1.8617 
1.8829 


.26496 
.26990 

.27482 


2.0947 
2.1132 
2.1320 


.32113 
.32495 
.32878 


.87869 
.88095 
.88317 


1.40 


4.0552 


.60801 


.24660 


1.9043 


.27974 


2.1509 


.33262 


.88535 


1.41 
1.42 
1.43 


4.0960 
4.1371 
4.1787 


.61236 
.61670 
.62104 


.24414 
.24171 
.23931 


1.9259 
1.9477 
1.9697 


.28464 
.28952 
.29440 


2.1700 
2.1894 
2.2090 


.33647 
.34033 
.34420 


.88749 
.88960 
.89167 


1.44 
1.45 
1.46 


4.2207 
4.2631 
4.3060 


.62538 
.62973 
.63407 


.23693 
.23457 
.23224 


1.9919- 
2.0143 
2.0369 


.29926 
.30412 
.30896 


2.2288 
2.2488 
2.2691 


.34807 
.35196 
.35585 


.89370 
.89569 
.89765 


1.47 
1.48 
1.49 


4.3492 
4.3929 
4.4371 


.63841 
.64276 
.64710 


.22993 
.22764 
.22537 


2.0597 
2.0827 
2.1059 


.31379 
.31862 
.32343 


2.2896 
2.3103 
2.3312 


.35976 
.36367 
.36759 


.89958 
.90147 
.90332 


1.50 


4.4817 


.65144 


.22313 


2.1293 


.32823 


2.3524 


.37151 


.90515 



IX] Values and Logarithms of Hyperbolic Functions 119 



X 


Value Logio 


Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


1.50 


4.4817 


.65144 


.22313 


2.1293 


.32823 


2.3524 


.37151 


.90515 


1.51 
1.52 
1.53 


4.5267 
4.5722 
4.6182 


.65578 
.66013 
.66447 


.22091 
.21871 
.21654 


2.1529 
2.1768 
2.2008 


.33303 
.33781 
.34258 


2.3738 
2.3955 
2.4174 


.37545 
.37939 
.38334 


.90694 
.90870 
.91042 


1.54 
1.55 
1.56 


4.6646 
4.7115 

4.7588 


.66881 
.67316 
.67750 


.21438 
.21225 
.21014 


2.2251 
2.2496 
2.2743 


.34735 
.35211 
.35686 


2.4395 
2.4619 

2.4845 


.38730 
.39126 
.39524 


.91212 
.91379 
.91542 


1.57 
1.58 
1.59 


4.8066 
4.8550 
4.9037 


.68184 
.68619 
.69053 


.20805 
.20598 
.20393 


2.2993 
2.3245 
2.3499 


.36160 
.36633 
.37105 


2.5073 
2.5305 
2.5538 


.39921 
.40320 
.40719 


.91703 
.91860 
.92015 


1.60 


4.9530 


.69487 


.20190 


2.3756 


.37577 


2.5775 


.41119 


.92167 


1.61 
1.62 
1.63 


5.0028 
5.0531 
5.1039 


.69921 
.70356 
.70790 


.19989 
.19790 
.19593 


2.4015 
2.4276 
2.4540 


.38048 
.38518 
.38987 


2.6013 
2.6255 
2.6499 


.41520 
.41921 
.42323 


.92316 
.92462 
.92606 


1.64 
1.65 
1.66 


5.1552 
5.2070 
5.2593 


.71224 
.71659 
.72093 


.19398 
.19205 
.19014 


2.4806 
2.5075 
2.5346 


.39456 
.39923 
.40391 


2.6746 
2.6995 

2.7247 


.42725 
.43129 
.43532 


.92747 
.92886 
.93022 


1.67 
1.68 
1.69 


5.3122 
5.3656 
5.4195 


.72527 
.72961 
.73396 


.18825 
.18637 
.18452 


2.5620 
2.5896 
2.6175 


.40857 
.41323 
.41788 


2.7502 
2.7760 
2.8020 


.43937 
.44341 
.44747 


.93155 
.93286 
.93415 


1.70 


5.4739 


.73830 


.18268 


2.6456 


.42253 


2.8283 


.45153 


.93541 


1.71 
1.72 
1.73 


5.5290 
5.5845 
5.6407 


.74264 
.74699 
.75133 


.18087 
.17907 

.17728 


2.6740 
2.7027 
2.7317 


.42717 
.43180 
.43643 


2.8549 
2.8818 
2.9090 


.45559 
.45966 
.46374 


.93665 
.93786 
.93906 


1.74 
1.75 
1.76 


5.6973 
5.7546 
5.8124 


.75567 
.76002 
.76436 


.17552 
.17377 
.17204 


2.7609 
2.7904 
2.8202 


.44105 
.44567 
.45028 


2.9364 
2.9642 
2.9922 


.46782 
.47191 
.47600 


.94023 
.94138 
.94250 


1.77 

1.78 
1.79 


5.8709 
5.9299 
5.9895 


.76870 
.77304 
.77739 


.17033 
.16864 
.16696 


2.8503 
2.8806 
2.9112 


.45488 
.45948 
.46408 


3.0206 
3.0492 
3.0782 


.48009 
.48419 
.48830 


.94361 
.94470 
.94576 


1.80 


6.0496 


.78173 


.16530 


2.9422 


.46867 


3.1075 


.49241 


.94681 


1.81 

1.82 
1.83 


6.1104 
6.1719 
6.2339 


.78607 
.79042 
.79476 


.16365 
.16203 
.16041 


2.9734 
3.0049 
3.0367 


.47325 
.47783 
.48241 


3.1371 
3.1669 
3.1972 


.49652 
.50064 
.50476 


.94783 
.94884 
.94983 


1.84 
1.85 
1.86 


6.2965 
6.3598 
6.4237 


.79910 
.80344 
.80779 


.15882 
.15724 
.15567 


3.0689 
3.1013 
3.1340 


.48698 
.49154 
.49610 


3.2277 
3.2585 
3.2897 


.50889 
.51302 
.51716 


.95080 
.95175 
.95268 


1.87 
1.88 
1.89 


6.4883 
6.5535 
6.6194 


.81213 

.81647 
.82082 


.15412 
.15259 
.15107 


3.1671 

3.2005 
3.2341 


.50066 
.50521 
.50976 


3.3212 
3.3530 
3.3852 


.52130 
.52544 
.52959 


.95359 
.95449 
.95537 


1.90 


6.6859 


.82516 


.14957 


3.2682 


.51430 


3.4177 


.53374 


.95624 


1.91 
1.92 
1.93 


6.7531 
6.8210 
6.8895 


.82950 
.83385 
.83819 


.14808 
.14661 
.14515 


3.3025 
3.3372 
3.3722 


.51884 
.52338 
.52791 


3.4506 
3.4838 
3.5173 


.53789 
.54205 
.54621 


.95709 
.95792 
.95873 


1.94 
1.95 
1.96 


6.9588 
7.0287 
7.0993 


.84253 
.84687 
.85122 


.14370 
.14227 
.14086 


3.4075 
3.4432 
3.4792 


.53244 
.53696 
.54148 


3.5512 

3.5855 
3.6201 


.55038 
.55455 

.55872 


.95953 
.96032 
.96109 


1.97 
1.98 
1.99 


7.1707 
7.2427 
7.3155 


.85556 
.85990 
.86425 


.13946 

.13807 
.13670 


3.5156 
3.5523 
3.5894 


.54600 
.55051 
.55502 


3.6551 
3.6904 
3.7261 


.56290 
.56707 
.57126 


.96185 
.96259 
.96331 


2.00 


7.3891 


.86859 


.13534 


3.6269 


.55953 


3.7622 


.57544 


.96403 1 



120 


Values and Logarithms of Hyperbolic Functions 


[IX 


X 


e x 
Value Logio 


e~ x 
Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


2.00 


7.3891 


.86859 


.13534 


3.6269 


.55953 


3.7622 


.57544 


.96403 


2.01 
2.02 
2.03 


7.4633 
7.5383 
7.6141 


.87293 
.87727 
.88162 


.13399 
.13266 
.13134 


3.6647 
3.7028 
3.7414 


.56403 
.56853 
.57303 


3.7987 
3.8355 
3.8727 


.57963 

.58382 
.58802 


.96473 
.96541 
.96609 


2.04 
2.05 
2.06 


7.6906 
7.7C79 
7.8460 


.88596 
.89030 
.89465 


.13003 
.12873 
.12745 


3.7803 
3.8196 
3.8593 


.57753 
.58202 
.58650 


3.9103 
3.9483 
3.9867 


.59221 
.59641 
.60061 


.96675 
.96740 
.96803 


2.07 
2.08 
2.09 


7.9248 
8.0045 
8.0849 


.89899 
.90333 
.90768 


.12619 
.12493 
.12369 


3.8993 
3.9398 
3.9806 


.59099 

.59547 
.59995 


4.0255 
4.0647 
4.1043 


.60482 
.60903 
.61324 


.96865 
.96926 
.96986 


2.10 


8.1662 


.91202 


.12246 


4.0219 


.60443 


4.1443 


.61745 


.97045 


2.11 
2.12 
2.13 


8.2482 
8.3311 
8.4149 


.91636 
.92070 
.92505 


.12124 
.12003 
.11884 


4.0635 
4.1056 
4.1480 


.60890 
.61337 
.61784 


4.1847 
4.2256 
4.2669 


.62167 
.62589 
.63011 


.97103 
.97159 
.97215 


2.14 
2.15 
2.16 


8.4994 
8.5849 
8.6711 


.92939 
.93373 
.93808 


.11765 
.11648 
.11533 


4.1909 
4.2342 
4.2779 


.62231 
.62677 
.63123 


4.3085 
4.3507 
4.3932 


.63433 
.63856 
.64278 


.97269 
.97323 
.97375 


2.17 
2.18 
2.19 


8.7583 
8.8463 
8.9352 


.94242 
.94676 
.95110 


.11418 
.11304 
.11192 


4.3221 

4.3666 
4.4116 


.63569 
,64015 
.64460 


4.4362 
4.4797 
4.5236 


.64701 
.65125 
.65548 


.97426 

.97477 
.97526 


2.20 


9.0250 


.95545 


.11080 


4.4571 


.64905 


4.5679 


.65972 


.97574 


2.21 
2.22 
2.23 


9.1157 
9.2073 
9.2999 


.95979 
.96413 

.96848 


.10970 
.10861 
.10753 


4.5030 
4.5494 
4.5962 


.65350 
.65795 
.66240 


4.6127 
4.6580 
4.7037 


.66396 
.66820 
.67244 


.97622 
.97668 
.97714 


2.24 
2.25 
2.26 


9.3933 
9.4877 
9.5831 


.97282 
.97716 
.98151 


.10646 
.10540 
.10435 


4.6434 
4.6912 
4.7394 


.66684 
.67128 
.67572 


4.7499 
4.7966 
4.8437 


.67668 
.68093 
.68518 


.97759 
.97803 
.97846 


2.27 
2.28 
2.29 


9.6794 
9.7767 
9.8749 


.98585 
.99019 
.99453 


.10331 
.10228 
.10127 


4.7880 
4.8372 
4.8868 


.68016 
.68459 
.68903 


4.8914 
4.9395 
4.9881 


.68943 
.69368 
.69794 


.97888 
.97929 
.97970 


2.30 


9.9742 


.99888 


.10026 


4.9370 


.69346 


5.0372 


.70219 


.98010 


2.31 
2.32 
2.33 


10.074 
10.176 
10.278 


.00322 
.00756 
.01191 


.09926 
.09827 
.09730 


4.9876 
5.0387 
5.0903 


.69789 
.70232 
.70675 


5.0868 
5.1370 
5.1876 


.70645 
.71071 
.71497 


.98049 
.98087 
.98124 


2.34 
2.35 
2.36 


10.381 
10.486 
10.591 


.01625 
.02059 
.02493 


.09633 
.09537 
.09442 


5.1425 
5.1951 
5.2483 


.71117 
.71559 
.72002 


5.2388 
5.2905 
5.3427 


.71923 
.72349 
.72776 


.98161 
.98197 
.98233 


2.37 
2.38 
2.39 


10.697 
10.805 
10.913 


.02928 
.03362 
.03796 


.09348 
.09255 
.09163 


5.3020 
5.3562 
5.4109 


.72444 
.72885 
.73327 


5.3954 

5.4487 
5.5026 


.73203 
.73630 
.74056 


.98267 
.98301 
.98335 


2.40 


11.023 


.04231 


.09072 


5.4662 


.73769 


5.5569 


.74484 


.98367 


2.41 
2.42 
2.43 


11.134 
11.246 
11.359 


.04665 
.05099 
.05534 


.08982 
.08892 
.08804 


5.5221 
5.5785 
5.6354 


.74210 
.74652 
.75093 


5.6119 
5.6674 
5.7235 


.74911 
.75338 
.75766 


.98400 
.98431 
.98462 


2.44 
2.45 
2.46 


11.473 

11.588 
11.705 


.05968 
.06402 
.06836 


.08716 
.08629 
.08543 


5.6929, 
5.7510 
5.8097 


.75534 
.75975 
.76415 


5.7801 
5.8373 
5.8951 


.76194 
.76621 
.77049 


.98492 
.98522 
.98551 


2.47 
2.48 
2.49 


11.822 
11.941 
12.061 


.07271 
.07705 
.08139 


.08458 
.08374 
.08291 


5.8689 
5.9288 
5.9892 


.76856 
.77296 
.77737 


5.9535 
6.0125 
6.0721 


.77477 
.77906 
.78334 


.98579 
.98607 
.98635 


2.50 


12.182 


.08574 


.08208 


6.0502 


.78177 


6.1323 


.78762 


.98661 



IX] 


Values and Logarithms of Hyperbolic Functions 


121 


X 


e 

Value 


X 

Logio 


Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanhx 

Value 


2.50 


12.182 


.08574 


.08208 


6.0502 


.78177 


6.1323 


.78762 


.98661 


2.51 
2.52 
2.53 


12.305 
12.429 
12.554 


.09008 
.09442 
.09877 


.08127 
.08046 
.07966 


6.1118 
6.1741 
6.2369 


.78617 
.79057 
.79497 


6.1931 
6.2545 
6.3166 


.79191 
.79619 
.80048 


.98688 
.98714 
.98739 


2.54 
2.55 
2.56 


12.680 
12.807 
12.036 


.10311 
.10745 
.11179 


.07887 
.07808 
.07730 


6.3004 
6.3645 
6.4293 


.79937 
.80377 
.80816 


6.3793 
6.4426 
6.5066 


.80477 
.80906 
.81335 


.98764 

.98788 
.98812 


2.57 

2.58 
2.59 


13.066 
13.197 
13.330 


.11614 
.12048 
.12482 


.07654 
.07577 
.07502 


6.4946 
6.5607 
6.6274 


.81256 
.81695 
.82134 


6.5712 
6.6365 
6.7024 


.81764 
.82194 
.82623 


.98835 

.98858 
.98881 


2.60 


13.464 


.12917 


.07427 


6.6947 


.82573 


6.7690 


.83052 


.98903 


2.61 
2.62 
2.63 


13.599 
13.736 
13.874 


.13351 
.13785 
.14219 


.07353 
.07280 
.07208 


6.7628 
6.8315 
6.9008 


.83012 
.83451 
.83890 


6.8363 
6.9043 
6.9729 


.83482 
.83912 
.84341 


.98924 
.98946 
.98966 


2.64 
2.65 
2.66 


14.013 
14.154 
14.296 


.14654 
.15088 
.15522 


.07136 
.07065 
.06995 


6.9709 
7.0417 
7.1132 


.84329 

.84768 
.85206 


7.0423 
7.1123 
7.1831 


.84771 
.85201 
.85631 


.98987 
.99007 
.99026 


2.67 
2.68 
2.69 


14.440 
14.585 
14.732 


.15957 
.16391 
.16825 


.06925 
.06856 
.06788 


• 7.1854 
7.2583 
7.3319 


.85645 
.86083 
.86522 


7.2546 
7.3268 
7.3998 


.86061 
.86492 
.86922 


.99045 
.99064 
.99083 


2.70 


14.880 


.17260 


.06721 


7.4063 


.86960 


7.4735 


.87352 


.99101 


2.71 
2.72 
2.73 


15.029 
15.180 
15.333 


.17694 
.18128 
.18562 


.06654 
.06587 
.06522 


7.4814 
7.5572 
7.6338 


.87398 
.87836 

.88274 


7.5479 
7.6231 
7.6991 


.87783 
.88213 
.88644 


.99118 
.99136 
.99153 


2.74 
2.75 
2.76 


15.487 
15.643 
15.800 


.18997 
.19431 
.19865 


.06457 
.06393 
.06329 


7.7112 
7.7894 
7.8683 


.88712 
.89150 
.89588 


7.7758 
7.8533 
7.9316 


.89074 
.89505 
.89936 


.99170 
.99186 
.99202 


2.77 
2.78 
2.79 


15.959 
16.119 
16.281 


.20300 
.20734 
.21168 


.06266 
.06204 
.06142 


7.9480 

8.0285 
8.1098 


.90026 
.90463 
.90901 


8.0106 
8.0905 
8.1712 


.90367 

.90798 
.91229 


.99218 
.99233 
.99248 


2.80 


16.445 


.21602 


.06081 


8.1919 


.91339 


8.2527 


.91660 


.99263 


2.81 

2.82 
2.83 


16.610 
16.777 
16.945 


.22037 
.22471 
.22905 


.06020 
.05961 
.05901 


8.2749 
8.3586 
8.4432 


.91776 
.92213 
.92651 


8.3351 
8.4182 
8.5022 


.92091 
.92522 
.92953 


.99278 
.99292 
.99306 


2.84 
2.85 
2.86 


17.116 

17.288 
17.462 


.23340 
.23774 
.24208 


.05843 

.05784 
.05727 


8.5287 
8.6150 
8.7021 


.93088 
.93525 
.93963 


8.5871 
8.6728 
8.7594 


.93385 
.93816 
.94247 


.99320 
.99333 
.99346 


2.87 
2.88 
2.89 


17.637 
17.814 
17.993 


.24643 

.25077 
.25511 


.05670 
.05613 
.05558 


8.7902 
8.8791 
8.9689 


.91100 
.94837 
.95274 


8.8469 
8.9352 
9.0244 


.94679 
.95110 
.95542 


.99359 
.99372 
.99384 


2.90 


18.174 


.25945 


.05502 


9.0596 


.95711 


9.1146 


.95974 


.99396 


2.91 
2.92 
2.93 


18.357 
18.541 

18.728 


.26380 
.26814 

.27248 


.05448 
.05393 
.05340 


9.1512 
9.2437 
9.3371 


.96148 
.96584 
.97021 


9.2056 
9.2976 
9.3905 


.96405 
.96837 
.97269 


.99408 
.99420 
.99431 


2.94 
2.95 
2.96 


18.916 
19.106 
19.298 


.27683 
.28117 
.28551 


.05287 
.05234 
.05182 


9.4315 
9.5268 
9.6231 


.97458 
.97895 
.98331 


9.4844 
9.5791 
9.6749 


.97701 
.98133 
.98565 


.99443 
.99454 
.99464 


2.97 

2.98 
2.99 


19.492 
19.688 
19.886 


.28985 
.29420 
.29854 


.05130 
.05079 
.05029 


9.7203 
9.8185 
9.9177 


.98768 
.99205 
.99641 


9.7716 
9.8693 
9.9680 


.98997 
.99429 
.99861 


.99475 
.99485 
.99496 


3.00 


20.086 


.30288 


1 .04979 


10.018 


.00078 


10.068 


.00293 


.99505 



122 


Values and Logarithms of Hyperbolic Functions 


px 


X 


Value Logio 


Value 


Sinh x 

Value Logio 


Cosh x 

Value Logio 


Tanh* 

Value 


3.00 


20.086 


.30288 


.04979 


10.018 


.00078 


10.068 


.00293 


.99505 


3.05 
3.10 
3.15 


21.115 
22.198 
23.336 


.32460 
.34631 
.36803 


.04736 
.04505 
.04285 


10.534 
11.076 
11.647 


.02259 
.04440 
.06620 


10.581 
11.122 
11.689 


.02454 
.04616 
.06779 


.99552 
.99595 
.99633 


3.20 
3.25 
3.30 


24.533 
25.790 
27.113 


.38974 
.41146 
.43317 


.04076 
.03877 
.03688 


12.246 

12.876 
13.538 


.08799 
.10977 
.13155 


12.287 
12.915 
13.575 


.08943 
.11108 
.13273 


.99668 
.99700 
.99728 


3.35 
3.40 
3.45 


28.503 
29.964 
31.500 


.45489 
.47660 

.49832 


.03508 
.03337 
.03175 


14.234 
14.965 
15.734 


.15332 

.17509 
.19685 


14.269 
14.999 
15.766 


.15439 
.17605 
.19772 


.99754 
.99777 
.99799 


3.50 


33.115 


.52003 


.03020 


16.543 


.21860 


16.573 


.21940 


.99818 


3.55 
3.60 
3.65 


34.813 
36.598 
38.475 


.54175 
.56346 
.58517 


.02872 
.02732 
.02599 


17.392 

18.285 
19.224 


.24036 
.26211 
.28385 


17.421 
18.313 
19.250 


.24107 
.26275 
.28444 


.99835 
.99851 
.99865 


3.70 
3.75 
3.80 


40.447 
42.521 
44.701 


.60689 
.62860 
.65032 


.02472 
.02352 
.02237 


20.211 
21.249 
22.339 


.30559 
.32733 
.34907 


20.236 
21.272 
22.362 


.30612 
.32781 
.34951 


.99878 
.99889 
.99900 


3.85 
3.90 
3.95 


46.993 
49.402 
51.935 


.67203 
.69375 
.71546 


.02128 
.02024 
.01925 


23.486 
24.691 
25.958 


.37081 
.39254 
.41427 


23.507 
24.711 
25.977 


.37120 
.39290 
.41459 


.99909 
.99918 
.99926 


4.00 


54.598 


.73718 


.01832 


27.290 


.43600 


27.308 


.43629 


.99933 


4.10 
4.20 
4.30 


60.340 
66.686 
73.700 


.78061 
.82404 
.86747 


.01657 
.01500 
.01357 


30.162 
33.336 
36.843 


.47946 
.52291 
.56636 


30.178 
33.351 
36.857 


.47970 
.52310 
.56652 


.99945 
.99955 
.99963 


4.40 
4.50 
4.60 


81.451 
90.017 
99.484 


.91090 
.95433 
.99775 


.01228 
.01111 
.01005 


40.719 

45.003 
49.737 


.60980 
.65324 
.69668 


40.732 
45.014 
49.747 


.60993 
.65335 
.69677 


.99970 
.99975 
.99980 


4.70 
4.80 
4.90 


109.95 
121.51 
134.29 


.04118 
.08461 
.12804 


.00910 
.00823 
.00745 


54.969 

60.751 
67.141 


.74012 
.78355 
.82699 


54.978 
60.759 
67.149 


.74019 
.78361 
.82704 


.99983 
.99986 
.99989 


5.00 


148.41 


.17147 


.00674 


74.203 


.87042 


74.210 


.87046 


.99991 


5.10 
5.20 
5.30 


164.02 
181.27 
200.34 


.21490 
.25833 
.30176 


.00610 
.00552 
.00499 


82.008 
90.633 
100.17 


.91386 
.95729 
.00072 


82.014 
90.639 
100.17 


.91389 
.95731 
.00074 


.99993 
.99994 
.99995 


5.40 
5.50 
5.60 


221.41 
244.63 
270.43 


.34519 
.38862 
.43205 


.00452 
.00409 
.00370 


110.70 
122.34 
135.21 


.04415 
.08758 
.13101 


110.71 
122.35 
135.22 


.04417 
.08760 
.13103 


.99996 
.99997 
.99997 


5.70 
5.80 
5.90 


298.87 
330.30 
365.04 


.47548 
.51891 
.56234 


.00335 
.00303 
.00274 


149.43 
165.15 

182.52 


.17444 

.21787 
.26130 


149.44 
165.15 
182.52 


.17445 

.21788 
.26131 


.99998 
.99998 
.99998 


6.00 


403.43 


.60577 


.00248 


201.71 


.30473 


201.72 


.30474 


.99999 


6.25 
6.50 
6.75 


518.01 
665.14 
854.06 


.71434 
.82291 
.93149 


.00193 
.00150 
.00117 


259.01 
332.57 
427.03 


.41331 
.52188 
.63046 


259.01 
332.57 
427.03 


.41331 
.52189 
.63046 


.99999 
1.0000 
1.0000 


7.00 
7.50 
8.00 


1096.6 
1808.0 
2981.0 


.04006 
.25721 
.47436 


.00091 
.00055 
.00034 


548.32 
904.02' 
1490.5 


.73903 
.95618 
.17333 


548.32 
904.02 
1490.5 


.73903 
.95618 
.17333 


1.0000 
1.0000 
1.0000 


8.50 
9.00 
9.50 


4914.8 
8103.1 
13360. 


.69150 
.90865 
.12580 


.00020 
.00012 
.00007 


2457.4 
4051.5 
6679.9 


.39047 
.60762 

.82477 


2457.4 
4051.5 
6679.9 


.39047 
.60762 

.82477 


1.0000 
1.0000 
1.0000 


10.00 


22026. 


.34294 


.00005 


11013. 


.04191 


11013. 


.04191 


1.0000 



X] Table X — Values and Logarithms of Haversines 

[Characteristics of Logarithms omitted — determine by rule from the value] 



123 



0' 

Value Logio 



10' 

Value Logio 



20' 
Value Logio 



30' 
Value Logio 



40' 
Value Logio 



50' 
Value Logio 



9 

10 

11 
12 
13 
14 

15 

16 

17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 
46 

47 
48 
49 

50 

51 

52 
53 
54 

55 

56 
57 

58 
59 



.0000 

00015.8817 
0003 .4837 
0007 .8358 
0012 .0856 



00004.3254 
00016.0156 
0004 .5532 
0008 .8828 
0013 .1211 



00004.9275 
00016.1315 
0004 .6176 
0008 .9273 
0014 .1551 



00005.2796 
0002 .2338 
0005 .6775 
0009 .9697 
0015 .1879 



00005.5295 
0002 .3254 
0005 .7336 
0010 .0101 
0017 .2195 



0001 5.7223 
0003 .4081 
0006 .7862 
0011 .0487 
0018 .2499 



0019 
.0027 
.0037 
.0049 
.0062 

.0076 
.0092 
.0109 
.0128 
.0149 

.0170 
0194 
.0218 
.0245 
.0272 

.0302 
.0332 
.0364 
.0397 
.0432 

.0468 
.0506 
.0545 
.0585 
.0627 

.0670 
.0714 
.0760 
.0807 
.0855 

0904 
.0955 
.1007 
.1060 
.1114 

.1170 
1226 
.1284 
.1343 
.1403 

1464 
.1527 
.1590 
.1654 
.1720 

.1786 
.1853 
.1922 
.1991 
.2061 

.2132 
.2204 
.2277 
.2350 
.2425 



.2793 
.4376 
.5713 
.6872 
.7893 

.8806 
.9631 
.0385 
.1077 
.1718 

.2314 

.2871 
.3394 
.3887 
.4352 

.4793 
.5213 
.5612 
.5993 
.6357 

.6707 
.7042 
.7364 
.7673 
.7972 

.8260 

.8538 
.8807 
.9067 
.9319 

.9563 
.9800 
.0030 
.0253 
.0470 
.0681 
.0887 
.1087 
.1282 
.1472 

.1657 
.1838 
.2014 
.2186 
.2355 

.2519 
.2680 
.2837 
.2991 
.3141 

.3288 
.3432 
.3573 
.3711 

.3847 



0020 
0029 
0039 
0051 
0064 

0079 
0095 
0112 
,0131 
,0152 

,0174 
.0198 
,0223 
,0249 
,0277 

,0307 
,0337 
,0370 
0403 
,0438 

,0475 
,0512 
,0552 
,0592 
,0634 

,0677 
,0722 
,0767 
.0815 
,0863 

.0913 
.0963 
.1016 
,1069 
.1123 

.1179 
.1236 
.1294 
.1353 
.1413 

1475 
.1538 
.1600 
.1665 
.1731 

.1797 
.1865 
.1933 
.2003 
.2073 

.2144 
.2216 
.2289 
.2363 
.2437 



.3078 
.4614 
.5918 
.7051 
.8052 

.8949 
.9762 
.0504 
.1187 
.1320 

.2409 
.2961 
.3478 
.3966 
.4427 

.4865 
.5281 
.5677 
.6055 
.6417 

.6764 
.7096 
.7416 

.7724 
.8020 

.8307 
.8583 
.8851 
.9109 
.9360 

.9603 
.9838 
.0067 
.0289 
.0505 

.0716 
.0920 
.1119 
.1314 
.1503 

.1687 
.1867 
.2043 
.2215 
.2382 

.2546 
.2706 
.2863 
.3016 
•3166 

.3312 
.3456 
.3596 
.3734 
.3869 



0022 
0031 
0041 
0053 
0066 

,0081 
,0097 
,0115 
,0135 
,0156 

,0178 
,0202 
.0227 
,0254 
.0282 

.0312 
.0343 
.0375 
.0409 
.0444 

.0481 
.0519 
.0558 
.0599 
.0641 

.0684 
.0729 
.0775 
.0823 
.0871 
.0921 
.0972 
.1024 
.1078 
.1133 

.1189 
.1246 
.1304 
.1363 
.1424 

.1485 
.1548 
.1611 
.1676 
.1742 

.1808 
.1876 
.1945 
.2014 
.2085 

.2156 

.2228 
.2301 
.2375 
.2450 



.3354 

.4845 
.6117 
.7226 
.8208 

.9090 
.9890 
.0622 
.1296 
.1921 

.2504 
.3049 
.3561 
.4045 
.4502 

.4936 
.5348 
.5741 
.6116 
.6476 

.6820 
.7151 

.7468 
.7774 
.8069 

.8354 
.8629 
.8894 
.9152 
.9401 

.9643 
.9877 
.0105 
.0326 
.0541 

.0750 
.0954 
.1152 
.1345 
.1534 

.1718 
.1897 
.2072 
.2243 
.2410 

.2573 
.2732 

.2888 
.3041 
.3190 

.3336 
.3480 
.3620 
.3757 
.3891 



0023 
0032 
0043 
,0055 
,0069 

,0084 
.0100 
.0119 
.0138 
.0159 

.0182 
.0206 
.0231 
.0258 
.0287 

.0317 
.0348 
.0381 
.0415 
.0450 

.0487 
.0525 
.0565 
.0606 
.0648 
.0692 
.0737 
.0783 
.0831 
.0879 

.0929 
.0981 
.1033 
.1087 
.1142 

.1198 
.1255 
.1314 
.1373 
.1434 

.1495 
.1558 
.1622 
.1687 
.1753 

.1820 
.1887 
.1956 
.2026 
.2096 

.2168 
.2240 
.2314 
.2388 

.2462 



.3621 
.5071 
.6312 

.7397 
.8361 

.9229 
.0016 
.0738 
.1404 
.2021 

.2597 
.3137 
.3644 
.4123 
.4576 

.5006 
.5415 
.5805 
.6177 
.6534 

.6876 
.7204 
.7520 

.7824 
.8117 

.8400 

.8673 
.8938 
.9194 
.9442 

.9682 
.9915 
.0142 
.0362 
.0576 
.0784 

.1185 
.1377 
.1565 

.1748 
.1926 
.2101 
.2271 
.2437 

.2600 
.2759 
.2914 
.3066 
.3215 

.3361 
.3503 
.3643 
.3779 
.3913 



0024 
0034 
0045 
,0057 
,0071 

.0086 
.0103 
.0122 
.0142 
.0163 

.0186 
.0210 
.0236 
.0263 
.0292 

.0322 
.0353 
.0386 
.0421 
.0456 

.0493 
.0532 
.0572 
.0613 
.0655 

.0699 
.0744 
.0791 
.0839 

.0888 

.0938 
.0989 
.1042 
.1096 
.1151 

.1207 
.1265 
.1323 
.1383 
.1444 

.1506 
.1569 
.1633 
.1698 
.1764 

.1831 
.1899 
.1968 
.2038 
.2108 

.2180 
.2252 
.2326 
.2400 
.2475 



.3880 
.5290 
.6503 
.7566 
.8512 

.9365 
.0141 
.0853 
.1510 
.2120 

.2689 
.3223 
.3726 
.4200 
.4649 

.5075 
.5481 

.5868 
.6238 
.6592 

.6932 

.7258 
.7572 
.7874 
.8165 

.8446 
.8718 
.5981 
.9236 
.9482 

.9722 
.9954 
.0179 
.0398 
.0611 

.0817 
.1021 
.1217 
.1409 
.1596 

.1778 
.1956 
.2129 
.2299 
.2465 

.2627 
.2785 
.2940 
.3091 
.3239 

.3384 
.3527 
.3666 
.3802 
.3935 



,0026 
,0036 
.0047 
.0059 
.0073 

.0089 
.0106 
.0125 
.0145 
.0167 

.0190 
.0214 
.0240 
.0268 
.0297 

.0327 
.0359 
.0392 
.0426 
.0462 

.0500 
.0538 
.0578 
.0620 
.0663 

.0707 
.0752 
.0799 
.0847 
.0896 

.0946 
.0998 
.1051 
.1105 
.1160 

.1217 
.1275 
.1333 
.1393 
.1454 

.1516 
.1579 
.1644 
.1709 
.1775 

.1842 
.1910 
.1979 
.2049 
.2120 
.2192 
.2265 
.2338 
.2412 
.2487 



.4132 
.5504 
.6689 
.7731 
.8660 

.9499 
.0264 
.0966 
.1614 
.2218 

.2781 
.3309 
.3806 
.4276 
.4721 

.5144 
.5547 
.5931 
.6298 
.6650 

.6987 
.7311 
.7623 
.7923 
.8213 

.8492 
.8763 
.9024 
.9277 
.9523 

.9761 
.9992 
.0216 
.0434 
.0646 

.0853 
.1054 
.1249 
.1440 
.1626 

.1808 
.1985 
.2158 
.2327 
.2492 

.2653 
.2811 
.2965 
.3116 
.3264 

.3408 
.3550 
.3689 
.3824 
.3957 



124 Values and Logarithms of Haversines 

[Characteristics of Logarithms omitted — determine by rule from the value] 



CX 



o' 

Value Logio 



10' 
Value Logio 



20' 
Value Logio 



30' 
Value Logio 



40' 
Value Logio 



50' 
Value Logio 



60 

61 
62 
63 
64 

65 

66 
67 
68 
69 

70 

71 

72 
73 
74 

75 

76 

77 
78 
79 

80 

81 

82 
83 
84 

85 

86 

87 
88 
89 

90 

91 
92 
93 
94 

95 

96 
97 
98 
99 

100 

101 
102 
103 
104 

105 

106 
107 
108 
109 

110 

111 
112 
113 
114 

115 

116 
117 
118 
119 



.2500 
.2576 
2653 
2730 

2808 

2887 
2966 
.3046 
3127 
.3208 

.3290 
.3372 
3455 
3538 
3622 

.3706 
.3790 
3875 
3960 
4046 

4132 
.4218 
.4304 
4391 
4477 
.4564 
4651 
.4738 
4826 
4913 

.5000 
5087 
.5174 
.5262 
.5349 

5436 
.5523 
.5609 
.5696 

5782 

.5868 
.5954 
.6040 
.6125 
.6210 
.6294 
.6378 
.6462 
.6545 
.6628 

.6710 
.6792 
.6873 
.6954 
.7034 

.7113 

.7192 
.7270 
.7347 

.7424 



.3979 
.4109 
.4237 
.4362 
.4484 

.4604 
.4722 
.4838 
.4951 
.5063 

.5172 
.5279 
.5384 

.5488 
.5589 

.5689 

.5787 
.5883 
.5977 
.6070 

.6161 
.6251 
.6339 
.6425 
.6510 
.6594 
.6676 
.6756 
.6835 
.6913 

.6990 
.7065 
.7139 
.7211 

.7283 

.7353 
.7421 
.7489 
.7556 
.7621 

.7685 

.7748 
.7810 
.7871 
.7931 

.7989 
.8047 
.8104 
.8159 
.8214 

.8267 
.8320 
.8371 

.8422 
.8472 

.8521 

.8568 
.8615 
.8661 
.8706 



,2513 
,2589 
,2665 
,2743 

,2821 

,2900 
.2980 
,3060 
,3140 
,3222 

,3304 
,3386 
,3469 
,3552 
,3636 

,3720 
,3805 
,3889 
,3975 
,4060 

,4146 
,4232 
,4319 
,4405 
.4492 

.4579 

,4666 
.4753 
.4840 
.4937 

.5015 
.5102 
.5189 
.5276 
.5363 

.5450 
.5537 
.5624 
.5710 
.5797 

.5883 
.5968 
.6054 
.6139 
.6224 

.6308 
.6392 
.6476 
.6559 
.6642 

.6724 
.6805 
.6887 
.6967 
.7047 

.7126 

.7205 
.7283 
.7360 
.7437 



.4001 
.4131 
.4258 
.4382 
.4504 

.4624 
.4742 
.4857 
.4970 
.5081 

.5190 
.5297 
.5402 
.5505 
.5606 

.5705 
.5803 
.5899 
.5993 
.6085 

.6176 
.6266 
.6353 
.6440 
.6524 

.6607 
.6689 
.6770 
.6848 
.6926 

.7002 
.7077 
.7151 
.7223 

.7294 

.7364 
.7433 
.7500 
.7567 
.7632 

.7696 
.7759 
.7820 
.7881 
.7940 

.7999 
.8056 
.8113 
.8168 
.8223 

.8276 
.8329 
.8380 
.8430 
.8480 

.8529 
.8576 
.8623 
.8669 
.8714 



.2525 
.2601 
.2678 
.2756 
.2834 

.2913 
.2993 
.3073 
.3154 
.3235 

.3317 
.3400 
.3483 
.3566 
.3650 

.3734 
.3819 
.3904 
.3989 
.4075 

.4160 
.4247 
.4333 
.4420 
.4506 

.4593 
.4680 
.4767 
.4855 
.4942 

.5029 
.5116 
.5204 
.5291 
.5378 

.5465 
.5552 
.5638 
.5725 
.5811 

.5897 
.5983 
.6068 
.6153 
.6238 
.6322 
.6406 
.6490 
.6573 
.6655 

.6737 
.6819 
.6900 
.6980 
.7060 

.7139 
.7218 
.7296 
.7373 
.7449 



.4023 
.4152 
.4279 
.4403 
.4524 

.4644 
.4761 
.4876 
.4989 
.5099 

.5208 
.5314 
.5419 
.5522 
.5623 

.5722 

.5819 
.5915 
.6009 
.6101 

.6191 
.6280 
.6368 
.6454 
.6538 
.6621 
.6703 
.6783 
.6862 
.6939 

.7015 
.7090 
.7163 
.7235 
.7306 

.7376 
.7444 
.7511 

.7577 
.7642 

.7706 
.7769 
.7830 
.7891 
.7950 

.8009 
.8066 
.8122 

.8177 
.8232 

.8285 
.8337 
.8388 
.8439 
.8488 

.8537 

.8584 
.8631 
.8676 
.8721 



2538 
2614 
,2691 
2769 

,2847 

,2927 
,3006 
,3087 
,3167 
.3249 

.3331 
.3413 
.3496 
.3580 
.3664 

.3748 
.3833 
.3918 
.4003 
.4089 

.4175 
.4261 
.4347 
.4434 
.4521 

.4608 
.4695 
.4782 
.4869 
.4956 
.5044 
.5131 
.5218 
.5305 
.5392 

.5479 
.5566 
.5653 
.5739 

.5825 

.5911 

.5997 
.6082 
.6167 
.6252 

.6336 
.6420 
.6504 
.6587 
.6669 

.6751 
.'6833 
.6913 
.6994 
.7073 

.7153 
.7231 
.7309 
.7386 
.7462 



.4045 
.4173 
.4300 
.4423 
.4545 
.4664 
.4780 
.4895 
.5007 
.5117 

.5226 
.5332 
.5436 
.5539 
.5639 

.5738 
.5835 
.5930 
.6024 
.6116 

.6206 
.6295 
.6382 
.6468 
.6552 

.6635 
.6716 
.6796 
.6875 
.6952 

.7027 
.7102 
.7175 
.7247 
.7318 

.7387 
.7455 
.7523 
.7588 
.7653 

.7717 
.7779 
.7841 
.7901 
.7960 

.8018 
.8075 
.8131 
.8187 
.8241 

.8294 
.8346 
.8397 

.8447 
.8496 

.8545 
.8592 
.8638 
.8684 
.8729 



2551 

2627 
2704 
2782 
2861 

2940 
3020 
3100 
3181 
,3263 

,3345 
,3427 
,3510 
,3594 
,3678 
.3762 
.3847 
.3932 
.4017 
.4103 

.4189 
.4275 
.4362 
.4448 
.4535 

.4622 
.4709 
.4796 

.4884 
.4971 

.5058 
.5145 
.5233 
.5320 
.5407 

.5494 
.5580 
.5667 
.5753 

.5840 

.5925 
.6011 
.6096 
.6181 
.6266 
.6350 
.6434 
.6517 
.6600 
.6683 

.6765 
.6846 
.6927 
.7007 
.7087 

.7166 

.7244 
.7322 
.7399 

.7475 



.4066 
.4195 
.4320 
.4444 
.4565 

.4683 
.4799 
.4914 
.5026 
.5136 

.5244 
.5349 
.5454 
.5556 
.5656 

.5754 
.5851 
.5946 
.6039 
.6131 
.6221 
.6310 
.6397 
.6482 
.6566 

.6649 
.6730 
.6809 
.6887 
.6964 

.7040 
.7114 

.7187 
.7259 
.7329 

.7399 
.7467 
.7534 
.7599 
.7664 

.7727 
.7790 
.7851 
.7911 
.7970 

.8028 
.8085 
.8141 
.8196 
.8250 

.8302 
.8354 
.8405 
.8455 
.8504 

.8553 
.8600 
.8646 
.8691 
.8736 



2563 
2640 
2717 
2795 

2874 

2953 
3033 
3113 
,3195 
,3276 

.3358 
,3441 
.3524 
,3608 
.3692 

.3776 
.3861 
.3946 
.4032 
.4117 

.4203 
.4290 
.4376 
.4463 
.4550 

.4637 
.4724 
.4811 
.4898 
.4985 

.5073 
.5160 
.5247 
.5334 
.5421 

.5508 
.5595 
.5682 
.5768 
.5854 

.5940 
.6025 
.6111 
.6195 
.6280 

.6364 
.6448 
.6531 
.6614 
.6696 

.6778 
.6860 
.6940 
.7020 
.7100 

.7179 

.7257 
.7335 
.7411 

.7487 



.4088 
.4216 
.4341 
.4464 
.4584 

.4703 
.4819 
.4932 
.5044 
.5154 

.5261 
.5367 
.5471 
.5572 
.5672 

.5771 

.5867 
.5962 
.6055 
.6146 

.6236 
.6324 
.6411 
.6496 
.6580 
.6662 
.6743 
.6822 
.6900 
.6977 
.7052 
.7126 
.7199 
.7271 
.7341 

.7410 
.7478 
.7545 
.7610 
.7674 

.7738 
.7800 
.7861 
.7921 
.7980 

.8037 
.8094 
.8150 
.8205 

.8258 

.8311 
.8363 
.8414 
.8464 
.8513 

.8561 

.8608 
.8654 
.8699 
.8743 



X] 



Values and Logarithms of Haversines 

[Characteristics of Logarithms omitted — determine by rule from the value] 



125 



120 

121 
122 
123 
124 

125 

126 
127 
128 
129 

130 

131 
132 
133 
134 

135 

136 
137 
138 
139 

140 

141 
142 
143 
144 

145 

146 
147 

148 
149 

150 

151 
152 
153 
154 

155 

156 
157 
158 
159 

160 

161 
162 
163 
164 

165 

136 
167 
168 
169 

170 

171 
172 
173 
174 

175 

176 
177 

178 
179 



0' 

Value Logio 



.7500 
.7575 
.7650 
.7723 
.7796 

.7868 
.7939 
.8009 
.8078 
.8147 

.8214 
.8280 
.8346 
.8410 

.8473 

.8536 
.8597 
.8657 
.8716 

.8774 

.8830 
.8886 
.8940 
.8993 
.9045 

9096 
.9145 
.9193 
.9240 
.9286 

.9330 
9373 
9415 
.9455 
.9494 

.9532 
.9568 
.9603 
.9636 
.9668 

.9698 
.9728 
.9755 
.9782 
.9806 
.9830 
.9851 
.9872 
.9891 
.9908 

.9924 
.9938 
.9951 
.9963 
.9973 

.9981 
.9988 
.9993 
.9997 
.9999 



.8751 
.8794 
.8836 
.8878 
.8919 

.8959 
.8998 
.9036 
.9073 
.9110 

.9146 
.9180 
.9215 
.9248 
.9281 
.9312 
.9343 
.9374 
.9403 
.9432 

.9460 
.9487 
.9513 
.9539 
.9564 

.9588 
.9612 
.9635 
.9657 
.9678 

.9699 
.9719 
.9738 
.9757 
.9774 

.9792 
.9808 
.9824 
.9839 
.9853 

.9867 
.9880 
.9892 
.9904 
.9915 

.9925 
.9935 
.9944 
.9952 
.9960 

.9967 
.9973 
.9979 
.9984 
.9988 
.9992 
.9995 
.9997 
.9999 
.9999 



10' 
Value Logio 



.7513 

.7588 
.7662 
,7735 
.7808 

.7880 
.7951 
.8021 
,8090 
,8158 

,8225 
,8291 
,8356 

,8421 

,8484 

8546 
8607 
8667 
8725 
8783 

8840 
8895 
8949 
9002 
9054 

9104 
9153 
9201 
9248 
9293 

9337 
9380 
9422 
9462 
9500 

9538 
9574 
9608 
9641 
9673 

9703 
9732 
9760 
9786 
9810 

9833 
9855 

9875 
9894 
9911 

9927 
,9941 
,9953 
,9964 
,9974 
,9982 
,9989 
,9994 
,9997 
,9999 



.8758 
.8801 
.8843 
.8885 
.8925 

.8965 
.9004 
.9042 
.9079 
.9116 

.9151 
.9186 
.9220 
.9253 
.9286 

.9318 

.9348 
.9379 
.9408 
.9436 

.9464 
.9491 
.9518 
.9543 
.9568 

.9592 
.9616 
.9638 
.9660 
.9682 

.9702 
.9722 
.9741 
.9760 
.9777 

.9794 
.9811 
.9826 
.9841 
.9856 

.9869 
.9882 
.9894 
.9906 
.9917 

.9927 
.9937 
.9945 
.9954 
.9961 

.9968 
.9974 
.9980 
.9984 
.9988 
.9992 
.9995 
.9997 
.9999 
.9999 



20' 
Value Logio 



.7525 
.7600 
.7674 
.7748 
.7820 

.7892 
.7962 
,8032 
.8101 
,8169 

.8236 

,8302 
.8367 
.8431 
.8494 

,8556 
,8617 
,8677 
,8735 
,8793 

,8849 
8904 
8958 
9011 
9062 

9112 
9161 
9209 
9256 
9301 

9345 
9387 
9428 
9468 
9507 

9544 
9579 
9614 
9647 
9678 

,9708 
,9737 
,9764 
,9790 
,9814 

,9837 
,9858 
,9878 
,9897 
9914 

,9929 
9943 
,9955 
9966 
,9976 

,9983 
,9990 
,9995 
,9998 
9999 



.8765 
.8808 
.8850 
.8892 
.8932 

.8972 
.9010 
.9048 
.9085 
.9122 

.9157 
.9192 
.9226 
.9259 
.9291 

.9323 
.9353 
.9383 
.9413 
.9441 

.9469 
.9496 
.9522 
.9548 
.9572 

.9596 
.9620 
.9642 
.9664 
.9685 

.9706 
.9725 
.9744 
.9763 
.9780 

.9797 
.9813 
.9829 
.9844 
.9858 

.9871 

.9884 
.9896 
.9908 
.9919 

.9929 
.9938 
.9947 
.9955 
.9962 

.9969 
.9975 
.9981 
.9985 
.9989 

.9993 
.9996 
.9998 
.9999 
.9999 



30' 
Value Logio 



.7538 
.7612 
.7686 
.7760 
.7832 

.7904 
.7974 
.8044 
.8113 
.8180 

.8247 
.8313 
.8378 
.8442 
.8501 

.8566 

,8627 
.8686 
.8745 
.8802 

.8858 
.8913 
.8967 
.9019 
,9071 

,9121 
.9169 
.9217 
.9263 
,9308 
.9352 
.9394 
.9435 
.9475 
,9513 

.9550 

.9585 
.9619 
,9652 
,9683 

.9713 
.9742 
,9769 
,9794 
,9818 

.9841 
,9862 
,9881 
9900 
,9916 

,9931 
.9945 
,9957 
,9968 
,9977 

,9985 
,9991 
,9995 
,9998 
,9999 



.8772 
.8815 
.8857 
.8898 
.8939 

.8978 
.9017 
.9055 
.9092 
.9128 

.9163 
.9198 
.9231 
.9264 
.9297 

.9328 
.9359 

.9388 
.9417 
.9446 

.9473 
.9500 
.9526 
.9552 
.9576 

.9600 
.9623 
.9646 
.9668 
.9689 

.9709 
.9729 
.9747 
.9766 
.9783 
.9800 
.9816 
.9831 
.9846 
.9860 

.9874 
.9886 
.9898 
.9910 
.9920 

.9930 
.9940 
.9948 
.9956 
.9963 

.9970 
.9976 
.9981 
.9986 
.9990 

.9993 
.9996 
.9998 
.9999 
.9999 



40' 
Value Logio 



.7550 
.7625 
.7699 

.7772 
.7844 

.7915 

.7986 
.8055 
.8124 
.8192 

.8258 
.8324 
.8389 
.8452 
.8515 

.8576 
.8637 
.8696 

.8754 
.8811 

.8867 
.8922 
.8976 
.9028 
.9079 

.9129 
.9177 
.9225 
.9271 
.9316 

.9359 
.9401 
.9442 
.9481 
.9519 

.9556 
.9591 
.9625 
.9657 
.9688 

.9718 
.9746 

.9773 
.9798 
.9822 

.9844 
.9865 
.9885 
,9903 
,9919 

.9934 
.9947 
.9959 
.9969 
.9978 

.9986 
.9992 
.9996 
.9999 
,9999 



.8780 
.8822 
.8864 
.8905 
.8945 

.8985 
.9023 
.9061 
.9098 
.9134 

.9169 
.9203 
.9237 
.9270 
.9302 

.9333 
.9364 
.9393 
.9422 
.9450 

.9478 
.9505 
.9531 
.9556 
.9580 

.9604 
.9627 
.9650 
.9671 
.9692 

.9712 
.9732 
.9751 
.9769 
.9786 

.9803 
.9819 
.9834 
.9849 
.9863 

.9876 
.9888 
.9900 
.9911 
.9922 

.9932 
.9941 
.9950 
.9957 
.9965 

.9971 

.9977 
.9982 
.9987 
.9991 

.9994 
.9996 
.9998 
.9999 
.0000 



50' 
Value Logio 



.7563 
.7637 
.7711 

.7784 
.7856 

.7927 
.7997 
.8067 
.8135 
.8203 

.8269 
.8335 
.8399 
.8463 
.8525 

.8587 
.8647 
.8706 
.8764 
.8821 

.8877 
.8931 
.8984 
.9037 
.9087 

.9137 
.9185 
.9233 
.9278 
.9323 

.9366 

.9408 
.9448 
.9488 
.9525 
.9562 
.9597 
.9630 
.9663 
.9693 

.9723 
.9751 

.9777 
.9802 
.9826 

.9848 
.9869 
.9888 
.9905 
.9921 

.9936 
.9949 
.9961 
.9971 
.9980 

.9987 
.9992 
.9996 
.9999 
1.0000 



.8787 
.8829 
.8871 
.8912 
.8952 

.8991 
.9030 
.9067 
.9104 
.9140 

.9175 
.9209 
.9242 
.9275 
.9307 

.9338 
.9369 
.9398 
.9427 
.9455 

.9482 
.9509 
.9535 
.9560 
.9584 

.9608 
.9631 
.9653 
.9675 
.9695 

.9716 
.9735 
.9754 
.9772 
.9789 

.9805 

.9821 
.9836 
.9851 
.9865 

.9878 
.9890 
.9902 
.9913 
.9923 

.9933 
.9943 
.9951 
.9959 
.9966 
.9972 
.9978 
.9983 
.9987 
.9991 
.9994 
.9997 
.9998 
.9999 
.0000 



126 Table XI — Factor Table — Logarithms of Primes [XI 

[If iV Is prime, its logarithm Is given. If N is not prime, its factors are given.] 



N 


1 


3 


7 


9 


10 


0043213738 


0128372247 


0293837777 


0374264979 


11 


3-37 


0530784435 


3 2 - 13 


7-17 


12 


ll 2 


3-41 


1038037210 


3-43 


13 


1172712957 


7-19 


1367205672 


1430148003 


14 


3-47 


11-13 


3-7 2 


1731862684 


15 


1789769473 


3 2 -17 


1958996524 


3-53 


16 


7-23 


2121876044 


2227164711 


13 2 


17 


3 2 -19 


2380461031 


3-59 


2528530310 


18 


2576785749 


3-61 


11-17 


33.7 


19 


2810333672 


2855573090 


2944662262 


2988530764 


20 


3-67 


7-29 


3 2 -23 


11-19 


21 


3242824553 


3-71 


7-31 


3-73 


22 


13-17 


3483048630 


3560258572 


3598354823 


23 


3-7-11 


3673559210 


3-79 


3783979009 


24 


3820170426 


35 


13-19 


3-83 


25 


3996737215 


11-23 


4099331233 


7-37 


26 


3 2 -29 


4199557485 


3-89 


4297522800 


27 


4329692909 


3-7-13 


4424797691 


3 2 -31 


28 


4487063199 


4517864355 


7-41 


172 


29 


3-97 


4668676204 


33.ll 


13-23 


30 


7-43 


3-101 


4871383755 


3-103 


31 


4927603890 


4955443375 


5010592622 


11-29 


32 


3-107 


17-19 


3-109 


7-47 


33 


5198279938 


3 2 -37 


5276299009 


3-113 


34 


11-31 


73 


5403294748 


5428254270 


35 


33-13 


5477747054 


3-7-17 


5550944486 


36 


19 2 


3-11 2 


5646660643 


3 2 -41 


37 


7-53 


5717088318 


13-29 


5786392100 


38 


3-127 


5831987740 


3 2 -43 


5899496013 


39 


17-23 


3-131 


5987905068 


3-7-19 


40 


6031443726 


13-31 


11-37 


6117233080 


41 


3-137 


7-59 


3-139 


6222140230 


42 


6242820958 


3 2 -47 


7-61 


3-11-13 


43 


6344772702 


6364878964 


19-23 


6424645202 


44 


32.72 


6464037262 


3-149 


6522463410 


45 


11-41 


3-151 


6599162001 


33-17 


46 


6637009254 


6655809910 


6693168806 


7-67 


47 


3-157 


11-43 


3 2 -53 


6803355134 


48 


13-37 


3-7-23 


6875289612 


3-163 


49 


6910814921 


17-29 


7-71 


6981005456 


50 


3-167 


7015679851 


3-13 2 


7067177823 


51 


7-73 


3 3 -19 


11-47 


3-173 


52 


7168377233 


7185016889 


17-31 


23 2 


53 


3 2 -59 


13-41 


3-179 


7 2 -ll 


54 


7331972651 


3-181 


7379873263 


3 2 -61 


55 


19-29 


7-79 


7458551952 


13-43 


56 


3-11-17 


7505083949 


3 4 -7 


7551122664 


57 


7566361082 


3-191 


7611758132 


3-193 


58 


7-83 


11-53 


7686381012 


19-31 


59 


3-197 


7730546934 


3-199 


7774268224 


60 


7788744720 


3 2 -67 


7831886911 


3-7-29 


61 


13-47 


7874604745 


7902851640 


7916906490 


62 


3 3 -23 


7-89 


3-11-19 


17-37 


63 


8000293592 


3-211 


7 2 -13 


3 2 -71 


64 


8068580295 


8082109729 


8109042807 


11-59 


65 


3-7-31 


8149131813 


3 2 -73 


8188854146 


66 


8202014595 


3-13-17 


23-29 


3-223 


67 


11-61 


8280150642 


8305886687 


7-97 


68 


3-227 


8344207037 


3-229 


13-53 


69 


8394780474 3 2 -7-ll 


17-41 


3-233 



N 


LogN 


2 
3 
5 
7 
11 

13 
17 
19 
23 
29 

31 

37 
41 
43 

47 

53 
59 
61 
67 
71 

73 

79 
83 

89 
97 


301029995664 
477121254720 
698970004336 
845098040014 
041392685158 

113943352307 
230448921378 
278753600953 
361727836018 
462397997899 

491361693834 
568201724067 
612783856720 
633468455580 
672097857936 

724275869601 
770852011642 
785329835011 
826074802701 
851258348719 

863322860120 
897627091290 
919078092376 
949390006645 
986771734266 


1301 
1303 
1307 
1319 
1321 

1327 
1361 
1367 
1373 
1381 

1399 
1409 
1423 
1427 
1429 

1433 
1439 
1447 
1451 
1453 

1459 
1471 
1481 
1483 

1487 

1489 
1493 
1499 
1511 
1523 

1531 
1543 
1549 
1553 
1559 


1142772966 
1149444157 
1162755876 
1202447955 
1209028176 

1228709229 
1338581252 
1357685146 
1376705372 
1401936786 

1458177145 
1489109931 
1532049001 
1544239731 
1550322288 
1562461904 
1580607939 
1604685311 
1616674124 
1622656143 

1640552919 
1676126727 
1705550585 
1711411510 
1723109685 

1728946978 
1740598077 
1758016328 
1792644643 
1826999033 

1849751907 
1883659261 
1900514178 
1911714557 
1928461152 



XI] Factor Table — Logarithms of Primes 

[If N is a prime, its logarithm is given. If N is not a prime, its factors are given.] 



127 



N 


1 


3 


7 


9 


70 


8457180180 


19-37 


7-101 


8506462352 


71 


3 2 -79 


23-31 


3-239 


8567288904 


72 


7-103 


3-241 


8615344109 


36 


73 


17-43 


8651039746 


11-67 


8686444384 


74 


3-13-19 


8709888138 


3 2 -83 


7-107 


75 


8756399370 


3-251 


8790958795 


3-11-23 


76 


8813846568 


7-109 


13-59 


8859263398 


77 


3-257 


8881794939 


3-7-37 


19-41 


78 


11-71 


3 3 -29 


8959747324 


3-263 


79 


7-113 


13-61 


9014583214 


17-47 


80 


32-89 


11-73 


3-269 


9079485216 


81 


9090208542 


3-271 


19-43 


32-7-13 


82 


9143431571 


9153998352 


9175055096 


9185545306 


83 


3-277 


72.17 


3 3 -31 


9237619608 


84 


292 


3-281 


7-11 2 


3-283 


85 


23-37 


9309490312 


9329808219 


9339931638 


86 


3-7-41 


9360107957 


3- 17 2 


11-79 


87 


13-67 


32.97 


9429995934 


3-293 


88 


9449759084 


9459607036 


9479236198 


7-127 


89 


34-11 


19-47 


3-13-23 


29-31 


90 


17-53 


3-7-43 


9576072871 


32.101 


91 


9595183770 


11-83 


7-131 


9633155114 


92 


3-307 


13-71 


3 2 -103 


9680157140 


93 


7 2 -19 


3-311 


9717395909 


3-313 


94 


9735896234 


23-41 


9763499790 


13-73 


95 


3-317 


9790929006 


3-11-29 


7-137 


96 


31 2 


32.107 


9854264741 


3-17-19 


97 


9872192299 


7-139 


9898945637 


11-89 


98 


32-109 


9925535178 


3-7-47 


23-43 


99 


9960736545 


3-331 


9986951583 


33.37 


100 


7-11-13 


17-59 


19-53 


0038911662 


101 


3-337 


0056094454 


32-113 


0081741840 


102 


0090257421 


3-11-31 


13-79 


3-73 


103 


0132586653 


0141003215 


17-61 


0166155476 


104 


3-347 


7-149 


3-349 


0207754882 


105 


0216027160 


3 4 -13 


7-151 


3-353 


106 


0257153839 


0265332645 


11-97 


0289777052 


107 


32-7-17 


29-37 


3-359 


13-83 


108 


23-47 


3-192 


0362295441 


32-112 


109 


0378247506 


0386201619 


0402066276 


7-157 


110 


3-367 


0425755124 


33.41 


0449315461 


111 


11-101 


3-7-53 


0480531731 


3-373 


112 


19-59 


0503797563 


72-23 


0*26939419 


113 


3-13-29 


11-103 


3-379 


17-67 


114 


7-163 


32-127 


31-37 


3-383 


115 


0610753236 


0618293073 


13-89 


19-61 


116 


3 3 -43 


0655797147 


3-389 


7-167 


117 


0685568951 


3-17-23 


11-107 


32-131 


118 


0722498976 


7-132 


0744507190 


29-41 


119 


3-397 


0766404437 


32-7-19 


11-109 


120 


0795430074 


3-401 


17-71 


3-13-31 


121 


7-173 


0838608009 


0852905782 


23-53 


122 


3-11-37 


0874264570 


3-409 


0895518829 


123 


0902580529 


3 2 -137 


0923696996 


3-7-59 


124 


17-73 


11-113 


29-43 


0965624384 


125 


32-139 


7-179 


3-419 


1000257301 


126 


13-97 


3-421 


7-181 


33.47 


127 


31-41 


19-67 


1061908973 


1068705445 


128 


3-7-61 


1082266564 


32-11-13 


1102529174 


129 


1109262423 


3-431 


1129399761 


3-433 



N 


LogN 


1567 


1950689965 


1571 


1961761850 


1579 


1983821300 


1583 


1994809149 


1597 


2033049161 


1601 


2043913319 


1607 


2060158768 


1609 


2065560441 


1613 


2076343674 


1619 


2092468488 


1621 


2097830148 


1627 


2113875529 


1637 


2140486794 


1657 


2193225084 


1663 


2208922492 


1667 


2219355998 


1669 


2224563367 


1693 


2286569581 


1697 


2296818423 


1699 


2301933789 


1709 


2327420627 


1721 


2357808703 


1723 


2362852774 


1733 


2387985627 


1741 


2407987711 


1747 


2422929050 


1753 


2437819161 


1759 


2452658395 


1777 


2496874278 


1783 


2511513432 


1787 


2521245525 


1789 


2526103406 


1801 


2555137128 


1811 


2579184503 


1823 


2607866687 


1831 


2626883443 


1847 


2664668954 


1861 


2697463731 


1867 


2711443179 


1871 


2720737875 


1873 


2725377774 


1877 


2734642726 


1879 


2739267801 


1889 


2762319579 


1901 


2789821169 


1907 


2803506930 


1913 


2817149700 


1931 


2857822738 


1933 


2862318540 


1949 


2898118391 


1951 


2902572694 


1973 


2961270853 


1979 


2964457942 


1987 


2981978671 


1993 


2995072987 


1997 


3003780649 


1999 


3008127941 


2003 


3016809493 


2011 


3034120706 


2017 


3047058982 



128 



Table XII a — Compound interest: (1 + r) 



n 



[XII a 





Amount of 


One Dollar Principal at Compound Interest After 


n Years 




n 


2% 


2\% 


3% 


3\% 


4% 


4J% 


5% 


6% 


7% 


1 
2 
3 

4 
5 
6 

7 
8 
9 


1.0200 
1.0404 
1.0612 

1.0824 
1.1041 
1.1262 

1.1487 
1.1717 
1.1951 


1.0250 
1.0506 
1.0769 

1.1038 
1.1314 
1.1597 

1.1887 
1.2184 
1.2489 


1.0300 
1.0609 
1.0927 

1.1255 
1.1593 
1.1941 

1.2299 
1.2668 
1.3048 


1.0350 
1.0712 
1.1087 

1.1475 
1.1877 
1.2293 

1.2723 
1.3168 
1.3629 


1.0400 
1.0816 
1.1249 

1.1699 
1.2167 
1.2653 

1.3159 
1.3686 
1.4233 


1.0450 
1.0920 
1.1412 

1.1925 
1.2462 
1.3023 

1.3609 
1.4221 
1.4861 


1.0500 
1.1025 
1.1576 

1.2155 
1.2763 
1.3401 

1.4071 
1.4775 
1.5513 


1.0600 
1.1236 
1.1910 

1.2625 
1.3382 
1.4185 

1.5036 
1.5938 
1.6895 


1.0700 
1.1449 
1.2250 

1.3108 
1.4026 
1.5007 

1.6058 
1.7182 
1.8385 


10 


1.2190 


1.2801 


1.3439 


1.4106 


1.4802 


1.5530 


1.6289 


1.7908 


1.9672 


11 
12 
13 

14 
15 
16 

17 
18 
19 


1.2434 
1.2682 
1.2936 

1.3195 
1.3459 
1.3728 

1.4002 
1.4282 
1.4568 


1.3121 
1.3449 
1.3785 

1.4130 
1.4483 
1.4845 

1.5216 
1.5597 
1.5987 


1.3842 
1.4258 
1.4685 

1.5126 
1.5580 
1.6047 

1.6528 
1.7024 
1.7535 


1.4600 
1.5111 
1.5640 

1.6187 
1.6753 
1.7340 

1.7947 
1.8575 
1.9225 


1.5395 
1.6010 
1.6651 

1.7317 
1.8009 
1.8730 

1.9479 

2.0258 
2.1068 


1.6229 
1.6959 
1.7722 

1.8519 
1.9353 
2.0224 

2.1134 

2.2085 
2.3079 


1.7103 
1.7959 
1.8856 

1.9799 
2.0789 
2.1829 

2.2920 
2.4066 
2.5270 


1.8983 
2.0122 
2.1329 

2.2609 
2.3966 
2.5404 

2.6928 
2.8543 
3.0256 


2.1049 
2.2522 
2.4098 

2.5785 
2.7590 
2.9522 

3.1588 
3.3799 
3.6165 


20 


1.4859 


1.6386 


1.8061 


1.9898 


2.1911 


2.4117 


2.6533 


3.2071 


3.8697 


21 
22 
23 

24 
25 
26 

27 
28 
29 


1.5157 
1.5460 
1.5769 

1.6084 
1.6406 
1.6734 

1.7069 
1.7410 

1.7758 


1.6796 
1.7216 
1.7646 

1.8087 
1.8539 
1.9003 

1.9478 
1.9965 
2.0464 


1.8603 
1.9161 
1.9736 

2.0328 
2.0938 
2.1566 

2.2213 

2.2879 
2.3566 


2.0594 
2.1315 
2.2061 

2.2833 
2.3632 
2.4460 

2.5316 
2.6202 
2.7119 


2.2788 
2.3699 
2.4647 

2.5633 
2.6658 
2.7725 

2.8834 
2.9987 
3.1187 


2.5202 
2.6337 
2.7522 

2.8760 
3.0054 
3.1407 

3.2820 
3.4297 
3.5840 


2.7860 
2.9253 
3.0715 

3.2251 
3.3864 
3.5557 

3.7335 
3.9201 
4.1161 


3.3996 
3.6035 
3.8197 

4.0489 
4.2919 
4.5494 

4.8223 
5.1117 
5.4184 


4.1406 
4.4304 
4.7405 

5.0724 
5.4274 
5.8074 

6.2139 

6.6488 
7.1143 


30 


1.8114 


2.0976 


2.4273 


2.8068 


3.2434 


3.7453 


4.3219 


5.7435 


7.6123 


31 
32 
33 

34 
35 
36 

37 

38 
39 


1.8476 

1.8845 
1.9222 

1.9607 
1.9999 
2.0399 

2.0807 
2.1223 
2.1647 


2.1500 
2.2038 
2.2589 

2.3153 
2.3732 
2.4325 

2.4933 
2.5557 
2.6196 


2.5001 
2.5751 
2.6523 

2.7319 
2.8139 

2.8983 

2.9852 
3.0748 
3.1670 


2.9050 
3.0067 
3.1119 

3.2209 
3.3336 
3.4503 

3.5710 
3.6960 
3.8254 


3.3731 
3.5081 
3.6484 

3.7943 
3.9461 
4.1039 

4.2681 
4.4388 
4.6164 


3.9139 
4.0900 
4.2740 

4.4664 
4.6673 

4.8774 

5.0969 
5.3262 
5.5659 


4.5380 
4.7649 
5.0032 

5.2533 
5.5160 

5.7918 

6.0814 
6.3855 
6.7048 


6.0881 
6.4534 
6.8406 

7.2510 
7.6861 
8.1473 

8.6361 
9.1543 
9.7035 


8.1451 
8.7153 
9.3253 

9.9781 
10.6766 
11.4239 

12.2236 
13.0793 
13.9948 


40 


2.2080 


2.6851 


3.2620 


3.9593 


4.8010 


5.8164 


7.0400 


10.2857 


14.9745 


41 
42 
43 

44 
45 
46 

47 
48 
49 


2.2522 

2.2972 
2.3432 

2.3901 
2.4379 
2.4866 

2.5363 
2.5871 

2.6388 


2.7522 
2.8210 
2.8915 

2.9638 
3.0379 
3.1139 

3.1917 
3.2715 
3.3533 


3.3599 
3.4607 
3.5645 

3.6715 
3.7816 
3.8950 

4.0119 
4.1323 
4.2562 


4.0978 
4.2413 
4.3897 

4.5433 

4.7024 
4.8669 

5.0373 
5.2136 
5.3961 


4.9931 
5.1928 
5.4005 

5.6165 
5.8412 
6.0748 

6.3178 
6.5705 
6.8333 


6.0781 
6.3516 
6.6374 

6.9361 

7.2482 
7.5744 

7.9153 
8.2715 
8.6437 


7.3920 
7.7616 
8.1497 

8.5572 
8.9850 
9.4343 

9.9060 
10.4013 
10.9213 


10.9029 
11.5570 
12.2505 

12.9855 
13.7646 
14.5905 

15.4659 
16.3939 
17.3775 


16.0227 
17.1443 
18.3444 

19.6285 
21.0025 
22.4726 

24.0457 
25.7289 
27.5299 


50 


2.6916 


3.4371 


4.3839 


5.5849 


7.1067 


9.0326 


11.4674 


18.4202 


29.4570 



XII b] Table XII b — Compound Discount: 1/(1 + r) n 129 

Present Value of One Dollar Due at the End op n Years 



n 


2% 


2\% 


3% 


3\% 


4% 


4i% 


5% 


6% 


7% 


1 
2 
3 

4 
5 
6 

7 
8 
9 


.98039 
.96117 
.94232 

.92385 
.90573 

.88797 

.87056 
.85349 
.83676 


.97561 
.95181 
.92860 

.90595 

.88385 
.86230 

.84127 
.82075 
.80073 


.97087 
.94260 
.91514 

.88849 
.86261 

.83748 

.81309 
.78941 
.76642 


.96618 
.93351 
.90194 

.87144 
.84197 
.81350 

.78599 
.75941 
.73373 


.96154 
.92456 
.88900 

.85480 
.82193 
.79031 

.75992 
.73069 
.70259 


.95694 
.91573 
.87630 

.83856 
.80245 
.76790 

.73483 
.70319 
.67290 


.95238 
.90703 
.86384 

.82270 
.78353 

.74622 

.71068 
.67684 
.64461 


.94340 
.89000 
.83962 

.79209 
.74726 
.70496 

.66506 
.62741 
.59190 


.93458 
.87344 
.81630 

.76290 
.71299 
.66634 

.62275 
.58201 
.54393 


10 


.82035 


.78120 


.74409 


.70892 


.67556 


.64393 


.61391 


.55839 


.50835 


11 
12 
13 

14 
15 
16 

17 

18 
19 


.80426 
.78849 
.77303 

.75788 
.74301 
.72845 

.71416 
.70016 
.68643 


.76214 
.74356 
.72542 

.70773 
.69047 
.67362 

.65720 
.64117 
.62553 


.72242 
.70138 
.68095 

.66112 
.64186 
.62317 

.60502 
.58739 
.57029 


.68495 
.66178 
.63940 

.61778 
.59689 
.57671 

.55720 
.53836 
.52016 


.64958 
.62460 
.60057 

.57748 
.55526 
.53391 

.51337 
.49363 
.47464 


.61620 
.58966 
.56427 

.53997 
.51672 
.49447 

.47318 
.45280 
.43330 


.58468 
.55684 
.53032 

.50507 
.48102 
.45811 

.43630 
.41552 
.39573 


.52679 
.49697 

.46884 

.44230 
.41727 
.39365 

.37136 
.35034 
.33051 


.47509 
.44401 
.41496 

.38782 
.36245 
.33873 

.31657 

.29586 
.27651 


20 


.67297 


.61027 


.55368 


.50257 


.45639 


.41464 


.37689 


.31180 


.25842 


21 
22 
23 

24 
25 
26 

27 
28 
29 


.65978 
.64684 
.63416 

,62172 
.60953 
.59758 

.58586 
.57437 
.56311 


.59539 
.58086 
.56670 

.55288 
.53939 
.52623 

.51340 

.50088 
.48866 


.53755 
.52189 
.50669 

.49193 
.47761 
.46369 

.45019 
.43708 
.42435 


.48557 
.46915 
.45329 

.43796 
.42315 

.40884 

.39501 
.38165 
.36875 


.43883 
.42196 
.40573 

.39012 
.37512 
.36069 

.34682 
.33348 
.32065 


.39679 
.37970 
.36335 

.34770 
.33273 
.31840 

.30469 
.29157 
.27902 


.35894 
.34185 
.32557 

.31007 
.29530 
.28124 

.26785 
.25509 
.24295 


.29416 
.27751 
.26180 

.24698 
.23300 
.21981 

.20737 
.19563 
.18456 


.24151 
.22571 
.21095 

.19715 
.18425 
.17220 

.16093 
.15040 
.14056 


30 


.55207 


.47674 


.41199 


.35628 


.30832 


.26700 


.23138 


.17411 


.13137 


31 
32 
33 

34 
35 
36 

37 

38 
39 


.54125 
.53063 
.52023 

.51003 
.50003 
.49022 

.48061 
.47119 
.46195 


.46511 
.45377 
.44270 

.43191 
.42137 
.41109 

.40107 
.39128 
.38174 


.39999 
.38834 
.37703 

.36604 
.35538 
.34503 

.33498 
.32523 
.31575 


.34423 
.33259 
.32134 

.31048 
.29998 
.28983 

.28003 
.27056 
.26141 


.29646 
.28506 
.27409 

.26355 
.25342 
.24367 

.23430 
.22529 
.21662 


.25550 
.24450 
.23397 

.22390 
.21425 
.20503 

.19620 

.18775 
.17967 


.22036 
.20987 
.19987 

.19035 
.18129 
.17266 

.16444 
.15661 
.14915 


.16425 
.15496 
.14619 

.13791 
.13011 
.12274 

.11580 
.10924 
.10306 


.12277 
.11474 
.10723 

.10022 
.09366 
.08754 

.08181 
.07646 
.07146 


40 


.45289 


.37243 


.30656 


.25257 


.20829 


.17193 


.14205 


.09722 


.06678 


41 
42 
43 

44 
45 
46 

47 
48 
49 


.44401 
.43530 
.42677 

.41840 
.41020 
.40215 

.39427 
.38654 
.37896 


.36335 
.35448 
.34584 

.33740 
.32917 
.32115 

.31331 
.30567 

.29822 


.29763 
.28896 
.28054 

.27237 
.26444 
.25674 

.24926 
.24200 
.23495 


.24403 
.23578 

.22781 

.22010 
.21266 
.20547 

.19852 
.19181 
.18532 


.20028 
.19257 
.18517 

.17805 
.17120 
.16461 

.15828 
.15219 
.14634 


.16453 
.15744 
.15066 

.14417 
.13796 
.13202 

.12634 
.12090 
.11569 


.13528 

.12884 
.12270 

.11686 
.11130 
.10600 

.10095 
.09614 
.09156 


.09172 
.08653 
.08163 

.07701 

.07265 

1 .06854 

.06466 
.06100 
.05755 


.06241 
.05833 
.05451 

.05095 
.04761 
.04450 

.04159 
.03887 
.03632 


50 


.37153 


.29094 


.22811 


.17905 


.14071 


.11071 


.08720 


.05429 


.03395 



130 



Table XII c — Amount of an Annuity 



[XII c 







Amount op an Annuity op 


One Dollar per Year after n Years 




n 


2% 


2h% 


3% 


3h% 


4% 


4i% 


5% 


6% 


7% 


1 

2 
3 

4 
5 
6 

7 
8 
9 


1.0000 
2.0200 
3.0604 

4.1216 
5.2040 
6.3081 

7.4343 
8.5830 
9.7546 


1.0000 
2.0250 
3.0756 

4.1525 
5.2563 
6.3877 

7.5474 
8.7361 
9.9545 


1.0000 
2.0300 
3.0909 

4.1836 
5.3091 
6.4684 

7.6625 

8.8923 

10.1591 


1.0000 
2.0350 
3.1062 

4.2149 
5.3625 
6.5502 

7.7794 

9.0517 

10.3685 


1.0000 
2.0400 
3.1216 

4.2465 
5.4163 
6.6330 

7.8983 

9.2142 

10.5828 


1.0000 
2.0450 
3.1370 

4.2782 
5.4707 
6.7169 

8.0192 

9.3800 

10.8021 


1.0000 
2.0500 
3.1525 

4.3101 
5.5256 
6.8019 

8.1420 

9.5491 

11.0266 


1.0000 
2.0600 
3.1836 

4.3746 
5.6371 
6.9753 

8.3938 

9.8975 

11.4913 


1.0000 
2.0700 
3.2149 

4.4399 

5.7507 
7.1533 

8.6540 
10.2598 
11.9780 


10 


10.9497 


11.2034 


11.4639 


11.7314 


12.0061 


12.2882 


12.5779 


13.1808 


13.8164 


11 
12 
13 

14 
15 
16 

17 
18 
19 


12.1687 
13.4121 
14.6803 

15.9739 
17.2934 
18.6393 

20.0121 
21.4123 
22.8406 


12.4835 
13.7956 
15.1404 

16.5190 
17.9319 
19.3802 

20.8647 
22.3863 
23.9460 


12.8078 
14.1920 
15.6178 

17.0863 
18.5989 
20.1569 

21.7616 
23.4144 
25.1169 


13.1420 
14.6020 
16.1130 

17.6770 
19.2957 
20.9710 

22.7050 
24.4997 
26.3572 


13.4864 
15.0258 
16.6268 

18.2919 
20.0236 
21.8245 

23.6975 
25.6454 
27.6712 


13.8412 
15.4640 
17.1599 

18.9321 
20.7841 
22.7193 

24.7417 
26.8551 
29.0636 


14.2068 
15.9171 
17.7130 

19.5986 
21.5786 
23.6575 

25.8404 
28.1324 
30.5390 


14.9716 
16.8699 
18.8821 

21.0151 
23.2760 
25.6725 

28.2129 
30.9057 
33.7600 


15.7836 

17.8885 
20.1406 

22.5505 
25.1290 

27.8881 

30.8402 
33.9990 
37.3790 


20 


24.2974 


25.5447 


26.8704 


28.2797 


29.7781 


31.3714 


33.0660 


36.7856 


40.9955 


21 
22 
23 

24 
25 
26 

27 
28 
29 


25.7833 
27.2990 
28.8450 

30.4219 
32.0303 
33.6709 

35.3443 
37.0512 
38.7922 


27.1833 
28.8629 
30.5844 

32.3490 
34.1578 
36.0117 

37.9120 

39.8598 
41.8563 


28.6765 
30.5368 
32.4529 

34.4265 
36.4593 
38.5530 

40.7096 
42.9309 
45.2189 


30.2695 
32.3289 
34.4604 

36.6665 
38.9499 
41.3131 

43.7591 
46.2906 
48.9108 


31.9692 
34.2480 
36.6179 

39.0826 
41.6459 
44.3117 

47.0842 
49.9676 
52.9663 


33.7831 
36.3034 
38.9370 

41.6892 
44.5652 
47.5706 

50.7113 
53.9933 
57.4230 


35.7193 
38.5052 
41.4305 

44.5020 
47.7271 
51.1135 

54.6691 
58.4026 
62.3227 


39.9927 
43.3923 
46.9958 

50.8156 
54.8645 
59.1564 

63.7058 
68.5281 
73.6398 


44.8652 
49.0057 
53.4361 

58.1767 
63.2490 
68.6765 

74.4838 
80.6977 
87.3465 


30 


40.5681 


43.9027 


47.5754 


51.6227 


56.0849 


61.0071 


66.4388 


79.0582 


94.4608 


31 
32 
33 

34 
35 
36 

37 
38 
39 


42.3794 
44.2270 
46.1116 

48.0338 
49.9945 
51.9944 

54.0343 
56.1149 
58.2372 


46.0003 
48.1503 
50.3540 

52.6129 
54.9282 
57.3014 

59.7339 
62.2273 
64.7830 


50.0027 
52.5028 
55.0778 

57.7302 
60.4621 
63.2759 

66.1742 
69.1594 
72.2342 


54.4295 
57.3345 
60.3412 

63.4532 
66.6740 
70.0076 

73.4579 
77.0289 
80.7249 


59.3283 
62.7015 
66.2095 

69.8579 
73.6522 
77.5983 

81.7022 
85.9703 
90.4091 


64.7524 
68.6662 
72.7562 

77.0303 
81.4966 
86.1640 

91.0413 

96.1382 

101.4644 


70.7608 
75.2988 
80.0638 

85.0670 
90.3203 
95.8363 

101.6281 
107.7095 
114.0950 


84.8017 
90.8898 
97.3432 

104.1838 
111.4348 
119.1209 

127.2681 
135.9042 
145.0585 


102.0730 
110.2182 
118.9334 

128.2588 
138.2369 
148.9135 

160.3374 
172.5610 
185.6403 


40 


60.4020 


67.4026 


75.4013 


84.5503 


95.0255 


107.0303 


120.7998 


154.7620 


199.6351 


41 
42 
43 

44 
45 
46 

47 
48 
49 


62.6100 
64.8622 
67.1595 

69.5027 
71.8927 
74.3306 

76.8172 
79.3535 
81.9406 


70.0876 
72.8398 
75.6608 

78.5523 
81.5161 
84.5540 

87.6679 
90.8596 
94.1311 


78.6633 
82.0232 
85.4839 

89.0484 
92.7199 
96.5015 

100.3965 
104.4084 
108.5406 


88.5095 
92.6074 
96.8486 

101.2383 
105.7817 
110.4840 

115.3510 
120.3883 
125.6018 


99.8265 
104.8196 
110.0124 

115.4129 
121.0294 
126.8706 

132.9454 
139.2632 
145.8337 


112.8467 
118.9248 
125.2764 

131.9138 
138.8500 
146.0982 

153.6726 
161.5879 
169.8594 


127,8398 
135.2318 
142.9933 

151.1430 
159.7002 
168.6852 

178.1194 
188.0254 
198.4267 


165.0477 
175.9505 
187.5076 

199.7580 
212.7435 
226.5081 

241.0986 
256.5645 
272.9584 


214.6096 
230.6322 
247.7765 

266.1209 
285.7493 
306.7518 

329.2244 
353.2701 
378.9990 


50 


84.5794 


97.4843 


112.7969 


130.9979 


152.6671 


178.5030 


209.3480 


290.3359 


406.5289 



XII d] Table XII d — Present Value of an Annuity 



131 







Present Value of One Dollar per 


Year for n Years 






n 


2% 


21% 


3% 


3h% 


4% 


4h% 


5% 


6% 


7% 


1 

2 
3 

4 
5 
6 

7 
8 
9 


.9804 
1.9416 
2.8839 

3.8077 
4.7135 
5.6014 

6.4720 
7.3255 
8.1622 


.9756 
1.9274 
2.8560 

3.7620 
4.6458 
5.5081 

6.3494 
7.1701 
7.9709 


.9709 
1.9135 

2.8286 

3.7171 
4.5797 
5.4172 

6.2303 
7.0197 

7.7861 


.9662 
1.8997 
2.8016 

3.6731 
4.5151 
5.3286 

6.1145 
6.8740 
7.6077 


.9615 
1.8861 
2.7751 

3.6299 
4.4518 
5.2421 

6.0021 
6.7327 
7.4353 


.9569 

1.8727 
2.7490 

3.5875 
4.3900 
5.1579 

5.8927 
6.5959 

7.2688 


.9524 
1.8594 
2.7232 

3.5460 
4.3295 
5.0757 

5.7864 
6.4632 
7.1078 


.9434 
1.8334 
2.6730 

3.4651 
4.2124 
4.9173 

5.5824 
6.2098 
6.8017 


.9346 
1.8080 
2.6243 

3.3872 
4.1002 
4.7665 

5.3893 
5.9713 
6.5152 


10 


8.9826 


8.7521 


8.5302 


8.3166 


8.1109 


7.9127 


7.7217 


7.3601 


7.0236 


11 
12 
13 

14 
15 
16 

17 
18 
19 


9.7868 
10.5753 
11.3484 

12.1062 
12.8493 
13.5777 

14.2919 
14.9920 
15.6785 


9.5142 
10.2578 
10.9832 

11.6909 
12.3814 
13.0550 

13.7122 
14.3534 
14.9789 


9.2526 

9.9540 

10.6350 

11.2961 
11.9379 
12.5611 

13.1661 
13\7535 
14.3238 


9.0016 

9.6633 

10.3027 

10.9205 
11.5174 
12.0941 

12.6513 
13.1897 
13.7098 


8.7605 
9.3851 
9.9856 

10.5631 
11.1184 
11.6523 

12.1657 
12.6593 
13.1339 


8.5289 
9.1186 
9.6829 

10.2228 
10.7395 
11.2340 

11.7072 

12.1600 
12.5933 


8.3064 
8.8633 
9.3936 

9.8986 
10.3797 
10.8378 

11.2741 
11.6896 
12.0853 


7.8869 
8.3838 
8.8527 

9.2950 

9.7122 

10.1059 

10.4773 
10.8276 
11.1581 


7.4987 
7.9427 
8.3577 

8.7455 
9.1079 
9.4466 

9.7632 
10.0591 
10.3356 


20 


16.3514 


15.5892 


14.8775 


14.2124 


13.5903 


13.0079 


12.4622 


11.4699 


10.5940 


21 
22 
23 

24 
25 
26 

27 
28 
29 


17.0112 
17.6580 
18.2922 

18.9139 
19.5235 
20.1210 

20.7069 
21.2813 
21.8444 


16.1845 
16.7654 
17.3321 

17.8850 
18.4244 
18.9506 

19.4640 
19.9649 
20.4535 


15.4150 
15.9369 
16.4436 

16.9355 
17.4131 

17.8768 

18.3270 
18.7641 
19.1885 


14.6980 
15.1671 
15.6204 

16.0584 
16.4815 
16.8904 

17.2854 
17.6670 
18.0358 


14.0292 
14.4511 
14.8568 

15.2470 
15.6221 
15.9828 

16.3296 
16.6631 
16.9837 


13.4047 
13.7844 
14.1478 

14.4955 

14.8282 
15.1466 

15.4513 

15.7429 
16.0219 


12.8212 
13.1630 
13.4886 

13.7986 
14.0939 
14.3752 

14.6430 
14.8981 
15.1411 


11.7641 
12.0416 
12.3034 

12.5504 
12.7834 
13.0032 

13.2105 
13.4062 
13.5907 


10.8355 
11.0612 
11.2722 

11.4693 
11.6536 
11.8258 

11.9867 
12.1371 
12.2777 


30 


22.3965 


20.9303 


19.6004 


18.3920 


17.2920 


16.2889 


15.3725 


13.7648 


12.4090 


31 
32 
33 

34 
35 
36 

37 

38 
39 


22.9377 
23.4683 
23.9886 

24.4986 
24.9986 

25.4888 

25.9695 
26.4406 
26.9026 


21.3954 
21.8492 
22.2919 

22.7238 
23.1452 
23.5563 

23.9573 

24.3486 
24.7303 


20.0004 

20.3888 
20.7658 

21.1318 

21.4872 
21.8323 

22.1672 
22.4925 

22.8082 


18.7363 
19.0689 
19.3902 

19.7007 
20.0007 
20.2905 

20.5705 
20.8411 
21.1025 


17.5885 
17.8736 
18.1476 

18.4112 
18.6646 
18.9083 

19.1426 
19.3679 
19.5845 


16.5444 
16.7889 
17.0229 

17.2468 
17.4610 
17.6660 

17.8622 
18.0500 
18.2297 


15.5928 
15.8027 
16.0025 

16.1929 
16.3742 
16.5469 

16.7113 
16.8679 
17.0170 


13.9291 
14.0840 
14.2302 

14.3681 
14.4982 
14.6210 

14.7368 
14.8460 
14.9491 


12.5318 
12.6466 
12.7538 

12.8540 
12.9477 
13.0352 

13.1170 
13.1935 
13.2649 


40 


27.3555 


25.1028 


23.1148 


21.3551 


19.7928 


18.4016 


17.1591 


15.0463 


13.3317 


41 
42 
43 

44 
45 
46 

47 
48 
49 


27.7995 
28.2348 
28.6616 

29.0800 
29.4902 
29.8923 

30.2866 
30.6731 
31.0521 


25.4661 
25.8206 
26.1664 

26.5038 
26.8330 
27.1542 

27.4675 

27.7732 
28.0714 


23.4124 
23.7014 
23.9819 

24.2543 
24.5187 
24.7754 

25.0247 
25.2667 
25.5017 


21.5991 
21.8349 
22.0627 

22.2828 
22.4955 
22.7009 

22.8994 
23.0912 
23.2766 


19.9931 
20.1856 
20.3708 

20.5488 
20.7200 

20.8847 

21.0429 
21.1951 
21.3415 


18.5661 
18.7236 

18.8742 

19.0184 
19.1563 
19.2884 

19.4147 
19.5356 
19.6513 


17.2944 
17.4232 
17.5459 

17.6628 
17.7741 
17.8801 

17.9810 
18.0772 

18.1687 


15.1380 
15.2245 
15.3062 

15.3832 
15.4558 
15.5244 

15.5890 
15.6500 
15.7076 


13.3941 
13.4524 
13.5070 

13.5579 
13.6055 
13.6500 

13.6910 
13.7305 
13.7668 


50 


31.4236 


28.3623 


25.7298 


23.4556 


21.4822 


19.7620 


18.2559 


15.7619 


13.8007 



132 Table XII e — Logarithms for Interest Computations [XII e 



r 


I + r 


log (1 + r) 


\% 


1.005 


00216 60617 56508 


1% 


1.010 


00432 13737 82643 


ii% 


1.015 


00646 60422 49232 


2% 


1.020 


00860 01717 61918 


2J% 


1.025 


01072 38653 91773 


3% 


1.030 


01283 72247 05172 


3J% 


1.035 


01494 03497 92937 


4% 


1.040 


01703 33392 98780 


4J% 


1.045 


01911 62904 47073 


5% 


1.050 


02118 92990 69938 



r 


I + r 


log (1 + r) 


5$% 


1.055 


02325 24596 33711 


6% 


1.060 


02530 58652 64770 


6J% 


1.065 


02734 96077 74757 


7% 


1.070 


02938 37776 85210 


7|% 


1.075 


03140 84642 51624 


8% 


1.080 


03342 37554 86950 


si% 


1.085 


03542 97381 84548 


9% 


1.090 


03742 64979 40624 


9J% 


1.095 


03941 41191 76137 


10% 


1.100 


04139 26851 58225 



For Amount, A, of any principal, P, after n years: A = P(l + r) n . 
For present worth, P, of any amount, A, at the end of n years: P = A -5- (1 + r) n . 
To find logarithms and antilogarithms of A and P to many significant figures, use 
Table XI, p. 126, and Table I a, p. 20. 



Table XII f — American Experience Mortality Table 



on 100,000 living at age 10 



At 

Age 


Number 
Surviving 


Deaths 


At 

Age 


Number 
Surviving 


Deaths 


At 

Age 


Number 
Surviving 


Deaths 


At 
Age 


Number 
Surviving 


Deaths 


10 


100,000 


749 


35 


81,822 


732 


60 


57,917 


1,546 


85 


5,485 


1,292 


11 


99,251 


746 


36 


81,090 


737 


61 


56,371 


1,628 


86 


4,193 


1,114 


12 


98,505 


743 


37 


80,353 


742 


62 


54,743 


1,713 


87 


3,079 


933 


13 


97,762 


740 


38 


79,611 


749 


63 


53,030 


1,800 


88 


2,146 


744 


14 


97,022 


737 


39 


78,862 


756 


64 


51,230 


1,889 


89 


1,402 


555 


15 


96,285 


735 


40 


78,106 


765 


65 


49,341 


1,980 


90 


847 


385 


16 


95,550 


732 


41 


77,341 


774 


66 


47,361 


2,070 


91 


462 


246 


17 


94,818 


729 


42 


76,567 


785 


67 


45,291 


2,158 


92 


216 


137 


18 


94,089 


727 


43 


75,782 


797 


68 


43,133 


2,243 


93 


79 


58 


19 


93,362 


725 


44 


74,985 


812 


69 


40,890 


2,321 


94 


21 


18 


20 


92,637 


723 


45 


74,173 


828 


70 


38,569 


2,391 


95 


3 


3 


21 


91,914 


722 


46 


73,345 


848 


71 


36,178 


2,448 








22 


91,192 


721 


47 


72,497 


870 


72 


33,730 


2,487 








23 


90,471 


720 


48 


71,627 


896 


73 


31,243 


2,505 








24 


89,751 


719 


49 


70,731 


927 


74 


28,738 


2,501 








25 


89,032 


718 


50 


69,804 


962 


75 


26,237 


2,476 








26 


88,314 


718 


51 


68,842 


1,001 


76 


23,761 


2,431 








27 


87,596 


718 


52 


67,841 


1,044 


77 


21,330 


2,369 








28 


86,878 


718 


53 


66,797 


1,091 


78 


18,961 


2,291 








29 


86,160 


719 


54 


65,706 


1,143 


79 


16,670 


2,196 








30 


85,441 


720 


55 


64,563 


1,199 


80 


14,474 


2,091 








31 


84,721 


721 


56 


63,364 


1,260 


81 


12,383 


1,964 








32 


84,000 


723 


57 


62,104 


1,325 


82 


10,419 


1,816 








33 


83,277 


726 


58 


60,779 


1,394 


83 


8,603 


1,648 








34 


82,551 


729 


59 


59,385 


1,468 


84 


6,955 


1,470 









XIII] 



Table XIII — Important Constants 

Logarithms of Important Constants 



133 



71 = NUMBER 


Value op n 


Logio n 


IT 


3.14159265 


0.49714987 


1 -Mr 


0.31830989 


9.50285013 


7T2 


9.86960440 


0.99429975 


V^f 


1.77245385 


0.24857494 


e = Naperian Base 


2.71828183 


0.43429448 


M = logio e 


0.43429448 


9.63778431 


I + M = log* 10 


2.30258509 


0.36221569 


180 -T- v = degrees in 1 radian 


57.2957795 


1.75812263 


ir + 180 = radians in 1° 


0.01745329 


8.24187737 


7T -J- 10800 = radians in 1' 


0.0002908882 


6.46372612 


ir -i- 648000 = radians in 1" 


0.000004848136811095 


4.68557487 


sin 1" 


0.000004848136811076 


4.68557487 


tan 1" 


0.000004848136811133 


4.68557487 


centimeters in 1 ft. 


30.480 


1.4840158 


feet in 1 cm. 


0.032808 


8.5159842 


inches in 1 m. 


39.37 (exact legal value) 


1.5951654 


pounds in 1 kg. 


2.20462 


0.3433340 


kilograms in 1 lb. 


0.453593 


9.6566660 


g (average value) 


32.16 ft./sec./sec. 


1.5073 , 




= 981 cm./sec./sec. 


2.9916690 


weight of 1 cu. ft. of water 


62.425 lb. (max. density) 


1.7953586 


weight of 1 cu. ft. of air 


0.0807 lb. (at 32° F.) 


8.907 


cu. in. in 1 (U. S.) gallon 


231 (exact legal value) 


2.3636120 


ft. lb. per sec. in 1 H. P. 


550 (exact legal value) 


2.7403627 


kg. m. per sec. in 1 H. P. 


76.0404 


1.8810445 


watts in 1 H. P. 


745.957 


2.8727135 



Several Numbers Vert Accurately 



7T 


= 3.14159 


26535 


89793 


23846 


26433 


83280 


e 


= 2.71828 


18284 


59045 


23536 


02874 


71353 


M 


= 0.43429 


44819 


03251 


82765 


11289 


18917 


1 +M 


= 2.30258 


50929 


94045 


68401 


79914 


54684 


logio 7T 


= 0.49714 


98726 


94133 


85435 


12682 


88291 


log 10 M 


= 9.63778 


43113 


00536 


78912 







Certain Convenient Values for n = 1 to n = 10 



n 


l/n 


■yjn 


■yjn 


n! 


l/n! 


Logio n 


1 


1.000000 


1.00000 


1.00000 


1 


1.0000000 


0.000000000 


2 


0.500000 


1.41421 


1.25992 


2 


0.5000000 


0.301029996 


3 


0.333333 


1.73205 


1.44225 


6 


0.1666667 


0.477121255 


4 


0.250000 


2.00000 


1.58740 


24 


0.0416667 


0.602059991 


5 


0.200000 


2.23607 


1.70998 


120 


0.0083333 


0.698970004 


6 


0.166667 


2.44949 


1.81712 


720 


0.0013889 


0.778151250 


7 


0.142857 


2.64575 


1.91293 


5040 


0.0001984 


0.845098040 


8 


0.125000 


2.82843 


2.00000 


40320 


0.0000248 


0.903089987 


9 


0.111111 


3.00000 


2.08008 


362880 


0.0000028 


0.954242509 


10 


0.100000 


3.16228 


2.15443 


3628800 


0.0000003 


1.000000000 



134 




Table XIV a - 


- Four Place Logarithms 


[XIV a 


N 

15 

11 
12 
13 

14 
15 

16 

17 

18 
19 





1 


2 


3 


4 


5 


6 


7 


8 


9 


1 2 3 


4 5 6 


7 8 9 


0000 


0043 


0086 


0128 


0170 


0212 


0253 


0294 


0334 


0374 


4 812 


17 2125 


29 33 37 


0414 
0792 
1139 

1461 
1761 
2041 

2304 
2553 

2788 


0453 
0828 
1173 

1492 
1790 
2068 

2330 

2577 
2810 


0492 
0864 
1206 

1523 
1818 
2095 

2355 
2601 
2833 


0531 
0899 
1239 

1553 
1847 
2122 

2380 
2625 
2856 


0569 
0934 
1271 

1584 
1875 
2148 

2405 

2648 
2878 


0607 
0969 
1303 

1614 
1903 
2175 

2430 
2672 
2900 


0645 
1004 
1335 

1644 
1931 
2201 

2455 
2695 
2923 


0682 
1038 
1367 

1673 
1959 
2227 

2480 
2718 
2945 


0719 
1072 
1399 

1703 
1987 
2253 

2504 

2742 
2967 


0755 
1106 
1430 

1732 
2014 
2279 

2529 
2765 
2989 


4 811 
3 710 
3 610 

3 6 9 
3 6 8 
3 5 8 

2 5 7 

2 5 7 

2 4 7 


15 19 23 
14 17 21 
13 16 19 

12 15 18 
11 1417 
111316 

10 12 15 
9 1214 
9 1113 


26 30 34 
24 28 31 
23 26 29 

21 24 27 
20 22 25 
18 21 24 

17 20 22 
16 19 21 
16 18 20 


20 

21 
22 
23 

24 
25 

26 

27 

28 
29 


3010 


3032 


3054 


3075 


3096 


3118 


3139 


3160 


3181 


3201 


2 4 6 


8 1113 


15 17 19 


3222 
3424 
3617 

3802 
3979 
4150 

4314 

4472 
4624 


3243 
3444 
3636 

3820 
3997 
4166 

4330 

4487 
4639 


3263 
3464 
3655 

3838 
4014 
4183 

4346 
4502 
4654 


3284 
3483 
3674 

3856 
4031 
4200 

4362 
4518 
4669 


3304 
3502 
3692 

3874 
4048 
4216 

4378 
4533 
4683 


3324 
3522 
3711 

3892 
4065 
4232 

4393 

4548 
4698 


3345 
3541 
3729 

3909 
4082 
4249 

4409 
4564 
4713 


3365 
3560 
3747 

3927 
4099 
4265 

4425 
4579 

4728 


3385 
3579 
3766 

3945 
4116 
4281 

4440 
4594 

4742 


3404 
3598 
3784 

3962 
4133 
4298 

4456 
4609 
4757 


2 4 6 

2 4 6 
2 4 6 

2 4 5 
2 4 5 
2 3 5 

2 3 5 
2 3 5 
1 3 4 


8 1012 
8 1012 
7 9 11 

7 911 

7 910 
7 810 

6 8 9 
6 8 9 
6 7 9 


14 16 18 
14 16 17 
13 15 17 

12 14 16 
12 14 16 
11 13 15 

11 12 14 
11 12 14 
10 12 13 


30 


4771 


4786 


4800 


4814 


4829 


4843 


4857 


4871 


4886 


4900 


13 4 


6 7 9 


10 11 13 


31 
32 
33 

34 
35 

36 

37 

38 
39 


4914 
5051 
5185 

5315 
5441 
5563 

5682 
5798 
5911 


4928 
5065 
5198 

5328 
5453 
5575 

5694 
5809 
5922 


4942 
5079 
5211 

5340 
5465 

5587 

5705 
5821 
5933 


4955 
5092 
5224 

5353 

5478 
5599 

5717 
5832 

5944 


4969 
5105 
5237 

5366 
5490 
5611 

5729 
5843 
5955 


4983 
5119 
5250 

5378 
5502 
5623 

5740 
5855 
5966 


4997 
5132 
5263 

5391 
5514 
5635 

5752 
5866 
5977 


5011 
5145 
5276 

5403 
5527 
5647 

5763 

5877 
5988 


5024 
5159 
5289 

5416 
5539 
5658 

5775 

5888 
5999 


5038 
5172 
5302 

5428 
5551 
5670 

5786 
5899 
6010 


1 3 4 
1 3 4 
13 4 

12 4 
12 4 
12 4 

12 4 
12 3 
12 3 


5 7 8 
5 7 8 
5 7 8 

5 6 8 
5 6 7 
5 6 7 

5 6 7 
5 6 7 
4 5 7 


10 11 12 
9 11 12 
9 il 12 

9 10 11 

9 10 11 
8 10 11 

8 9 11 

8 9 10 
8 9 10 


40 


6021 


6031 


6042 


6053 


6064 


6075 


6085 


6096 


6107 


6117 


12 3 


4 5 6 


8 9 10 


41 
42 
43 

44 
45 
46 

47 
48 
49 


6128 
6232 
6335 

6435 
6532 
6628 

6721 
6812 
6902 


6138 
6243 
6345 

6444 
6542 
6637 

6730 
6821 
6911 


6149 
6253 
6355 

6454 
6551 
6646 

6739 
6830 
6920 


6160 
6263 
6365 

6464 
6561 
6656 

6749 
6839 
6928 


6170 
6274 
6375 

6474 
6571 
6665 

6758 
6848 
6937 


6180 
6284 
6385 

6484 
6580 
6675 

6767 
6857 
6946 


6191 
6294 
6395 

6493 
6590 
6684 

6776 
6866 
6955 


6201 
6304 
6405 

6503 
6599 
6693 

6785 
6875 
6964 


6212 
6314 
6415 

6513 

6609 
6702 

6794 

6884 
6972 


6222 
6325 
6425 

6522 
6618 
6712 

6803 
6893 
6981 


12 3 
12 3 
12 3 

12 3 

12 3 
12 3 

12 3 
12 3 
12 3 


4 5 6 
4 5 6 
4 5 6 

4 5 6 
4 5 6 
4 5 6 

4 5 6 
4 5 6 
4 4 5 


7 8 9 
7 8 9 
7 8 9 

7 8 9 

7 8 9 
7 7 8 

7 7 8 
7 7 8 
6 7 8 


50 


6990 


6998 


7007 


7016 


7024 


7033 


7042 


7050 


7059 


7067 


12 3 


3 4 5 


6 7 8 


51 
52 
53 

54 
N 


7076 
7160 
7243 

7324 


7084 
7168 
7251 

7332 


7093 
7177 
7259 

7340 


7101 
7185 
7267 

7348 


7110 
7193 
7275 

7356 


7118 

7202 

7284 

7364 


7126 
7210 
7292 

7372 


7135 

7218 
7300 

7380 


7143 

7226 
7308 

7388 


7152 
7235 
7316 

7396 


12 3 
12 3 
12 2 

12 2 


3 4 5 
3 4 5 
3 4 5 

3 4 5 


6 7 8 
6 7 7 
6 6 7 

6 6 7 


|| 1 


2 


3 


4 | 5 


6 


7 8 


9 


12 3 


4 5 6 


7 8 9 



The proportional parts are stated in full for every tenth at the right-hand side. 
The logarithm of any number of four significant figures can be read directly by add- 



XIV a] Table XIV a — Four Place Logarithms 



135 



N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


12 3 


4 5 6 


7 8 9 


55 

56 

57 

58 
59 


7404 

7482 

7559 
7634 
7709 


7412 
7490 

7566 
7642 
7716 


7419 
7497 

7574 
7649 
7723 


7427 
7505 

7582 
7657 
7731 


7435 
7513 

7589 
7664 

7738 


7443 
7520 

7597 
7672 
7745 


7451 

7528 

7604 
7679 

7752 


7459 
7536 

7612 
7686 
7760 


7466 
7543 

7619 
7694 
7767 


7474 
7551 

7627 
7701 

7774 


12 2 
12 2 

112 
112 
112 


3 4 5 
3 4 5 

3 4 5 

3 4 4 
3 4 4 


5 6 7 
5 6 7 

5 6 7 
5 6 7 
5 6 7 


60 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 


112 


3 4 4 


5 6 6 


61 
62 
63 

64 
65 

66 

67 
68 
69 


7853 
7924 
7993 

8062 
8129 
8195 

8261 
8325 

8388 


7860 
7931 
8000 

8069 
8136 
8202 

8267 
8331 
8395 


7868 
7938 
8007 

8075 
8142 
8209 

8274 
8338 
8401 


7875 
7945 
8014 

8082 
8149 
8215 

8280 
8344 
8407 


7882 
7952 
8021 

8089 
8156 

8222 

8287 
8351 
8414 


7889 
7959 
8028 

8096 
8162 

8228 

8293 
8357 
8420 


7896 
7966 
8035 

8102 
8169 
8235 

8299 
8363 
8426 


7903 
7973 
8041 

8109 
8176 
8241 

8306 
8370 
8432 


7910 
7980 
8048 

8116 

8182 
8248 

8312 
8376 
8439 


7917 

7987 
8055 

8122 
8189 

8254 

8319 

8382 
8445 


112 
112 
112 

112 
112 
112 

112 
112 
112 


3 3 4 
3 3 4 
3 3 4 

3 3 4 
3 3 4 
3 3 4 

3 3 4 

3 3 4 
3 3 4 


5 6 6 
5 5 6 
5 5 6 

5 5 6 
5 5 6 
5 5 6 

5 5 6 
4 5 6 
4 5 6 


70 


8451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8506 


1 1 2 


3 3 4 


4 5 6 


71 

72 
73 

74 
75 

76 

77 
78 
79 


8513 
8573 
8633 

8692 
8751 

8808 

8865 
8921 
8976 


8519 
8579 
8639 

8698 
8756 
8814 

8871 
8927 
8982 


8525 

8585 
8645 

8704 
8762 
8820 

8876 
8932 
8987 


8531 
8591 
8651 

8710 

8768 
8825 

8882 
8938 
8993 


8537 
8597 
8657 

8716 

8774 
8831 

8887 
8943 
8998 


8543 
8603 
8663 

8722 
8779 
8837 

8893 
8949 
9004 


8549 
8609 
8669 

8727 
8785 
8842 

8899 
8954 
9009 


8555 
8615 
8675 

8733 
8791 

8848 

8904 
8960 
9015 


8561 
8621 

8681 

8739 

8797 
8854 

8910 
8965 
9020 


8567 
8627 
8686 

8745 
8802 
8859 

8915 
8971 
9025 


112 
112 

1 1 2 

112 
112 
112 

112 
112 
112 


3 3 4 
3 3 4 
2 3 4 

2 3 4 
2 3 3 
2 3 3 

2 3 3 
2 3 3 
2 3 3 


4 5 6 
4 5 6 
4 5 5 

4 5 5 
4 5 5 
4 4 5 

4 4 5 
4 4 5 

4 4 5 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


112 


2 3 3 


4 4 5 


81 

82 
83 

84 
85 

86 

87 
88 
89 


9085 
9138 
9191 

9243 
9294 
9345 

9395 
9445 
9494 


9090 
9143 
9196 

9248 
9299 
9350 

9400 
9450 
9499 


9096 
9149 
9201 

9253 
9304 
9355 

9405 
9455 
9504 


9101 
9154 
9206 

9258 
9309 
9360 

9410 
9460 
9509 


9106 
9159 
9212 

9263 
9315 
9365 

9415 
9465 
9513 


9112 
9165 
9217 

9269 
9320 
9370 

9420 
9469 
9518 


9117 
9170 
9222 

9274 
9325 
9375 

9425 
9474 
9523 


9122 
9175 
9227 

9279 
9330 
9380 

9430 
9479 
9528 


9128 
9180 
9232 

9284 
9335 
9385 

9435 
9484 
9533 


9133 
9186 
9238 

9289 
9340 
9390 

9440 
9489 
9538 


112 
1 1 2 
112 

1 1 2 
1 1 2 
1 1 2 

112 
1 1 
1 1 


2 3 3 
2 3 3 
2 3 3 

2 3 3 
2 3 3 
2 3 3 

2 3 3 
2 2 3 
2 2 3 


4 4 5 
4 4 5 
4 4 5 

4 4 5 
4 4 5 
4 4 5 

4 4 5 
3 4 4 
3 4 4 


90 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


1 1 


2 2 3 


3 4 4 


91 
92 
93 

94 
95 

96 

97 
98 
99 


9590 
9638 
9685 

9731 
9777 
9823 

9868 
9912 
9956 


9595 
9643 
9689 

9736 

9782 
9827 

9872 
9917 
9961 


9600 
9647 
9694 

9741 

9786 
9832 

9877 
9921 
9965 


9605 
9652 
9699 

9745 
9791 
9836 

9881 
9926 
9969 


9609 
9657 
9703 

9750 
9795 
9841 

9886 
9930 
9974 


9614 
9661 
9708 

9754 
9800 
9845 

9890 
9934 
9978 


9619 
9666 
9713 

9759 
9805 
9850 

9894 
9939 
9983 


9624 
9671 
9717 

9763 
9809 
9854 

9899 
9943 
9987 


9628 
9675 
9722 

9768 
9814 
9859 

9903 
9948 
9991 


9633 
9680 
9727 

9773 

9818 
9863 

9908 
9952 
9996 


Oil 
Oil 
1 1 

Oil 
1 1 
Oil 

Oil 
1 1 
Oil 


2 2 3 
2 2 3 
2 2 3 

2 2 3 
2 2 3 
2 2 3 

2 2 3 
2 2 3 
2 2 3 


3 4 4 
3 4 4 
3 4 4 

3 4 4 
3 4 4 
3 4 4 

3 4 4 
3 3 4 
3 3 4 


N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


12 3 


4 5 6 


7 8 9 



ing the proportional part corresponding to the fourth figure to the tabular number 
corresponding to the first three figures. There may be an error of 1 in the last place- 



136 




Table XIV b - 


■ Antiiogarithms to Four Places 


[XIV b 







l 


2 


3 


4 


5 


6 


7 


8 


9 


12 3 


4 5 6 


7 8 9 


.00 


1000 


1002 


1005 


1007 


1009 


1012 


1014 


1016 


1019 


1021 


1 


1 1 1 


2 2 2 


.01 
.02 
.03 

.04 
.05 

.06 

.07 
.08 
.09 


1023 
1047 
1072 

1096 
1122 
1148 

1175 
1202 
1230 


1026 
1050 
1074 

1099 
1125 
1151 

1178 
1205 
1233 


1028 
1052 
1076 

1102 
1127 
1153 

1180 
1208 
1236 


1030 
1054 
1079 

1104 
1130 
1156 

1183 
1211 
1239 


1033 
1057 
1081 

1107 
1132 
1159 

1186 
1213 
1242 


1035 
1059 
1084 

1109 
1135 
1161 

1189 
1216 
1245 


1038 
1062 
1086 

1112 
1138 
1164 

1191 
1219 
1247 


1040 
1064 
1089 

1114 
1140 
1167 

1194 
1222 
1250 


1042 
1067 
1091 

1117 
1143 
1169 

1197 
1225 
1253 


1045 
1069 
1094 

1119 
1146 
1172 

1199 
1227 
1256 


1 
1 
1 

1 1 
1 1 
1 1 

Oil 
Oil 
11 


1 1 1 
1 1 1 
111 

1 1 2 
112 
112 

112 

1 1 2 
1 1 2 


2 2 2 
2 2 2 
2 2 2 

2 2 2 
2 2 2 
2 2 2 

2 2 2 
2 2 3 
2 2 3 


.10 


1259 


1262 


1265 


1268 


1271 


1274 


1276 


1279 


1282 


1285 


1 1 


1 1 2 


2 2 3 


.11 
.12 
.13 

.14 
.15 

.16 

.17 
.18 
.19 


1288 
1318 
1349 

1380 
1413 
1445 

1479 
1514 
1549 


1291 
1321 
1352 

1384 
1416 
1449 

1483 
1517 
1552 


1294 
1324 
1355 

1387 
1419 
1452 

1486 
1521 
1556 


1297 
1327 
1358 

1390 
1422 
1455 

1489 
1524 
1560 


1300 
1330 
1361 

1393 
1426 
1459 

1493 
1528 
1563 


1303 
1334 
1365 

1396 
1429 
1462 

1496 
1531 
1567 


1306 
1337 
1368 

1400 
1432 
1466 

1500 
1535 
1570 


1309 
1340 
1371 

1403 
1435 
1469 

1503 
1538 
1574 


1312 
1343 
1374 

1406 
1439 
1472 

1507 
1542 
1578 


1315 
1346 
1377 

1409 
1442 
1476 

1510 
1545 
1581 


1 1 
Oil 
Oil 

1 1 
1 1 
1 1 

Oil 
Oil 
Oil 


12 2 
12 2 
12 2 

12 2 
12 2 
12 2 

12 2 
12 2 
1 2 2 


2 2 3 
2 2 3 
2 3 3 

2 3 3 
2 3 3 
2 3 3 

2 3 3 
2 3 3 
2 3 3 


.20 


1585 


1589 


1592 


1596 


1600 


1603 


1607 


1611 


1614 


1618 


Oil 


1 2 2 


3 3 3 


.21 
.22 
.23 

.24 
.25 

.26 

.27 

.28 
.29 


1622 
1660 
1698 

1738 

1778 
1820 

1862 
1905 
1950 


1626 
1663 
1702 

1742 
1782 
1824 

1866 
1910 
1954 


1629 
1667 
1706 

1746 
1786 
1828 

1871 
1914 
1959 


1633 
1671 
1710 

1750 
1791 
1832 

1875 
1919 
1963 


1637 
1675 
1714 

1754 
1795 
1837 

1879 
1923 
1968 


1641 
1679 
1718 

1758 
1799 
1841 

1884 
1928 
1972 


1644 
1683 
1722 

1762 
1803 
1845 

1888 
1932 
1977 


1648 
1687 
1726 

1766 
1807 
1849 

1892 
1936 
1982 


1652 
1690 
1730 

1770 
1811 
1854 

1897 
1941 
1986 


1656 
1694 
1734 

1774 
1816 

1858 

1901 
1945 
1991 


1 1 
1 1 
Oil 

Oil 
1 1 
Oil 

Oil 
Oil 
Oil 


12 2 
2 2 2 
2 2 2 

2 2 2 
2 2 3 
2 2 3 

2 2 3 
2 2 3 
2 2 3 


3 3 3 
3 3 3 
3 3 3 

3 3 4 
3 3 4 
3 3 4 

3 3 4 
3 4 4 
3 4 4 


.30 


1995 


2000 


2004 


2009 


2014 


2018 


2023 


2028 


2032 


2037 


Oil 


2 2 3 


3 4 4 


.31 
.32 
.33 

.34 
.35 

.36 

.37 
.38 

.39 


2042 
2089 
2138 

2188 
2239 
2291 

2344 
2399 
2455 


2046 
2094 
2143 

2193 
2244 
2296 

2350 
2404 
2460 


2051 
2099 
2148 

2198 
2249 
2301 

2355 
2410 
2466 


2056 
2104 
2153 

2203 
2254 
2307 

2360 
2415 
2472 


2061 
2109 
2158 

2208 
2259 
2312 

2366 
2421 

2477 


2065 
2113 
2163 

2213 
2265 
2317 

2371 
2427 
2483 


2070 
2118 
2168 

2218 
2270 
2323 

2377 
2432 

2489 


2075 
2123 
2173 

2223 
2275 
2328 

2382 
2438 
2495 


2080 
2128 
2178 

2228 
2280 
2333 

2388 
2443 
2500 


2084 
2133 
2183 

2234 
2286 
2339 

2393 
2449 
2506 


Oil 
1 1 

1 1 

112 
112 

1 1 2 

112 
112 
112 


2 2 3 
2 2 3 
2 2 3 

2 3 3 
2 3 3 
2 3 3 

2 3 3 
2 3 3 
2 3 3 


3 4 4 
3 4 4 

3 4 4 

4 4 5 
4 4 5 
4 4 5 

4 4 5 
4 5 5 
4 5 5 


.40 


2512 


2518 


2523 


2529 


2535 


2541 


2547 


2553 


2559 


2564 


1 1 2 


2 3 4 


4 5 5 


.41 
.42 
.43 

.44 
.45 
.46 

.47 
1.48 
1.49 


2570 
2630 
2692 

2754 

2818 
2884 

2951 
3020 
3090 


2576 
2636 
2698 

2761 

2825 
2891 

2958 
3027 
3097 


2582 
2642 
2704 

2767 
2831 

2897 

2965 
3034 
3105 


2588 
2649 
2710 

2773 

2838 
2904 

2972 
3041 
3112 


2594 
2655 
2716 

2780 
2844 
2911 

2979 
3048 
3119 


2600 
2661 
2723 

2786 
2851 
2917 

2985 
3055 
3126 


2606 
2667 

2729 

2793 

2858 
2924 

2992 
3062 
3133 


2612 
2673 
2735 

2799 
2864 
2931 

2999 
3069 
3141 


2618 
2679 

2742 

2805 

2871 
2938 

3006 
3076 

3148 


2624 
2685 

2748 

2812 

2877 
2944 

3013 
3083 
3155 


112 
1 1 2 
112 

1 1 2 
1 1 2 
112 

112 
112 
1 1 2 


2 3 4 
2 3 4 

2 3 4 

3 3 4 
3 3 4 
3 3 4 

3 3 4 
3 3 4 
3 4 4 


4 5 6 
4 5 6 
4 5 6 

4 5 6 

5 5 6 
5 5 6 

5 6 6 
5 6 6 
5 6 6 



XIV b] 


Table XIV b - 


- Antilogarithms to Four Places 


137 







l 


2 


3 


4 


5 


6 


7 


8 


9 


12 3 


4 5 6 


7 8 9 


.50 


3162 


3170 


3177 


3184 


3192 


3199 


3206 


3214 


3221 


3228 


112 


3 4 4 


5 6 7 


.51 
.52 
.53 

.54 
.55 

.56 

.57 

.58 
.59 


3236 
3311 

3388 

3467 
3548 
3631 

3715 

3802 
3890 


3243 
3319 
3396 

3475 
3556 
3639 

3724 
3811 
3899 


3251 
3327 
3404 

3483 
3565 
3648 

3733 
3819 
3908 


3258 
3334 
3412 

3491 
3573 
3656 

3741 

3828 
3917 


3266 
3342 
3420 

3499 
3581 
3664 

3750 
3837 
3926 


3273 
3350 

3428 

3508 
3589 
3673 

3758 
3846 
3936 


3281 
3357 
3436 

3516 
3597 
3681 

3767 
3855 
3945 


3289 
3365 
3443 

3524 
3606 
3690 

3776 
3864 
3954 


3296 
3373 
3451 

3532 
3614 
3698 

3784 
3873 
3963 


3304 
3381 
3459 

3540 
3622 
3707 

3793 

3882 
3972 


112 
112 
12 2 

12 2 
12 2 
12 2 

12 3 
12 3 
1 2 3 


3 4 4 
3 4 5 
3 4 5 

3 4 5 
3 4 5 
3 4 5 

3 4 5 

3 4 5 

4 5 5 


5 6 7 

5 6 7 

6 6 7 

6 6 7 

6 7 7 
6 7 8 

6 7 8 
6 7 8 
6 7 8 


.60 


3981 


3990 


3999 


4009 


4018 


4027 


4036 


4046 


4055 


4064 


1 2 3 


4 5 6 


7 8 8 


.61 
.62 
.63 

.64 
.65 
.66 

.67 
.68 
.69 


4074 
4169 
4266 

4365 
4467 
4571 

4677 
4786 
4898 


4083 
4178 
4276 

4375 

4477 
4581 

4688 
4797 
4909 


4093 
4188 
4285 

4385 

4487 
4592 

4699 
4808 
4920 


4102 
4198 
4295 

4395 
4498 
4603 

4710 
4819 
4932 


4111 
4207 
4305 

4406 
4508 
4613 

4721 
4831 
4943 


4121 
4217 
4315 

4416 
4519 
4624 

4732 

4842 
4955 


4130 
4227 
4325 

4426 
4529 
4634 

4742 
4853 
4966 


4140 
4236 
4335 

4436 
4539 
4645 

4753 
4864 
4977 


4150 
4246 
4345 

4446 
4550 
4656 

4764 

4875 
4989 


4159 
4256 
4355 

4457 
4560 
4667 

4775 

4887 
5000 


12 3 
12 3 

12 3 

12 3 
12 3 
12 3 

12 3 
12 3 
12 3 


4 5 6 
4 5 6 
4 5 6 

4 5 6 
4 5 6 
4 5 6 

4 5 7 

5 6 7 
5 6 7 


7 8 9 
7 8 9 
7 8 9 

7 8 9 
7 8 9 

7 9 10 

8 9 10 
8 9 10 
8 9 10 


.70 


5012 


5023 


5035 


5047 


5058 


5070 


5082 


5093 


5105 


5117 


12 3 


5 6 7 


8 9 10 


.71 

.72 
.73 

.74 
.75 

.76 

.77 
.78 
.79 


5129 

5248 
5370 

5495 
5623 
5754 

5888 
6026 
6166 


5140 
5260 
5383 

5508 
5636 
5768 

5902 
6039 
6180 


5152 
5272 
5395 

5521 
5649 
5781 

5916 
6053 
6194 


5164 

5284 
5408 

5534 
5662 
5794 

5929 
6067 
6209 


5176 
5297 
5420 

5546 
5675 
5808 

5943 
6081 
6223 


5188 
5309 
5433 

5559 
5689 
5821 

5957 
6095 
6237 


5200 
5321 
5445 

5572 
5702 
5834 

5970 
6109 
6252 


5212 
5333 
5458 

5585 
5715 

5848 

5984 
6124 
6266 


5224 
5346 
5470 

5598 

5728 
5861 

5998 
6138 
6281 


5236 
5358 
5483 

5610 
5741 
5875 

6012 
6152 
6295 


12 4 

12 4 

13 4 

13 4 
13 4 
13 4 

13 4 
13 4 
1 3 4 


5 6 7 
5 6 7 
5 6 7 

5 6 8 

5 7 8 
5 7 8 

5 7 8 

6 7 8 
6 7 9 


8 10 11 

9 10 11 
9 10 11 

9 10 12 
9 11 12 
9 11 12 

10 11 12 
10 11 13 
10 11 13 


.80 


6310 


6324 


6339 


6353 


6368 


6383 


6397 


6412 


6427 


6442 


13 4 


6 7 9 


10 12 13 


.81 

.82 
.83 

.84 
.85 

.86 

.87 
.88 
.89 


6457 
6607 
6761 

6918 
7079 
7244 

7413 
7586 
7762 


6471 
6622 
6776 

6934 
7096 
7261 

7430 
7603 

7780 


6486 
6637 
6792 

6950 
7112 

7278 

7447 
7621 
7798 


6501 
6653 
6808 

6966 
7129 
7295 

7464 
7638 
7816 


6516 
6668 
6823 

6982 
7145 
7311 

7482 
7656 
7834 


6531 
6683 
6839 

6998 
7161 
7328 

7499 
7674 

7852 


6546 
6699 
6855 

7015 

7178 
7345 

7516 
7691 

7870 


6561 
6714 
6871 

7031 
7194 
7362 

7534 
7709 

7889 


6577 
6730 

6887 

7047 
7211 
7379 

7551 

7727 
7907 


6592 
6745 
6902 

7063 

7228 
7396 

7568 
7745 
7925 


2 3 5 
2 3 5 
2 3 5 

2 3 5 
2 3 5 
2 3 5 

2 4 5 
2 4 5 

2 4 6 


6 8 9 
6 8 9 

6 8 9 

7 8 10 
7 8 10 
7 8 10 

7 9 10 
7 9 11 
7 9 11 


11 12 14 
11 12 14 
11 13 14 

11 13 15 

12 13 15 
12 14 15 

12 14 16 

12 14 16 

13 15 16 


.90 


7943 


7962 


7980 


7998 


8017 


8035 


8054 


8072 


8091 


8110 


2 4 6 


7 9 11 


13 15 17 


.91 
.92 
.93 

.94 
.95 

.96 

.97 
.98 
.99 


8128 
8318 
8511 

8710 
8913 
9120 

9333 
9550 
9772 


8147 
8337 
8531 

8730 
8933 
9141 

9354 
9572 
9795 


8166 
8356 
8551 

8750 
8954 
9162 

9376 
9594 
9817 


8185 
8375 
8570 

8770 
8974 
9183 

9397 
9616 
9840 


8204 
8395 
8590 

8790 
8995 
9204 

9419 
9638 
9863 


8222 
8414 
8610 

8810 
9016 
9226 

9441 
9661 

9886 


8241 
8433 
8630 

8831 
9036 
9247 

9462 
9683 
9908 


8260 
8453 
8650 

8851 
9057 
9268 

9484 
9705 
9931 


8279 
8472 
8670 

8872 
9078 
9290 

9506 
9727 
9954 


8299 
8492 
8690 

8892 
9099 
9311 

9528 
9750 
9977 


2 4 6 
2 4 6 
2 4 6 

2 4 6 
2 4 6 
2 4 6 

2 4 6 
2 4 7 
2 5 7 


8 9 11 
8 10 12 
8 10 12 

8 10 12 

8 10 12 

9 11 13 

9 11 13 
9 11 13 
9 11 14 


13 15 17 

14 15 17 
14 16 18 

14 16 18 

15 17 19 
15 17 19 

15 17 19 

16 18 20 
16 18 21 



138 Table XIV c — Four Place Trigonometric Functions [XIV c 

[Characteristics of Logarithms omitted — determine by the usual rule from the value] 



RADIANS 



.0000 
.0029 
.0058 
.0087 
.0116 
.0145 

.0175 
.0204 
.0233 
.0262 
.0291 
.0320 

.0349 
.0378 
.0407 
.0436 
.0465 
.0495 

.0524 
.0553 
.0582 
.0611 
.0640 
.0669 

.0698 
.0727 
.0756 
.0785 
.0814 
.0844 

.0873 
.0902 
.0931 
.0960 
.0989 
.1018 

.1047 
.1076 
.1105 
.1134 
.1164 
.1193 

.1222 
.1251 
.1280 
.1309 
.1338 
.1367 

.1396 
.1425 
.1454 
.1484 
.1513 
.1542 

.1571 



Degrees 



0°00' 

10 
20 
30 
40 
50 

1°00' 

10 
20 
30 
40 
1 50 

2° 00' 

10 
20 
30 
40 
50 

3° 00' 

10 
20 
30 
40 
50 

4° 00' 

10 
20 
30 
40 
50 

5° 00' 

10 
20 
30 
40 
50 

6° 00' 

10 
20 
30 
40 
50 

7° 00' 

10 
20 
30 
40 
50 

8° 00' 

10 
20 
30 
40 
50 

9° 00' 



Sine 
Value Logio 



.0000 
.0029 
.0058 
.0087 
.0116 
.0145 

.0175 
0204 
.0233 
0262 
.0291 
0320 

.0349 
.0378 
.0407 
.0436 
.0465 
.0494 

.0523 
.0552 
.0581 
.0610 
.0640 
.0669 

.0698 
.0727 
.0756 
.0785 
.0814 
0843 

0872 
0901 
0929 
0958 
0987 
1016 

1045 
1074 
1103 
1132 
1161 
1190 

1219 
1248 
1276 
1305 
1334 
,1363 

,1392 
,1421 
,1449 
.1478 
.1507 
.1536 

.1564 



.4637 
.7648 
.9408 
.0658 
.1627 

.2419 
.3088 
.3668 
.4179 
.4637 
.5050 

.5428 

.5776 
.6097 
.6397 
.6677 
.6940 

.7188 
.7423 
.7645 
.7857 
.8059 
.8251 

.8436 
.8613 
.8783 
.8946 
.9104 
.9256 

.9403 
.9545 
.9682 
.9816 
.9945 
.0070 

.0192 
.0311 
.0426 
.0539 
.0648 
.0755 

.0859 
.0961 
.1060 
.1157 
.1252 
.1345 

.1436 
.1525 
.1612 
.1697 

.1781 
.1863 

.1943 



Tangent 
Value Logio 



.0000 
.0029 
.0058 
.0087 
.0116 
.0145 

.0175 
.0204 
.0233 
.0262 
.0291 
.0320 

.0349 
.0378 
.0407 
.0437 
.0466 
.0495 

.0524 
.0553 
.0582 
.0612 
.0641 
.0670 

.0699 
.0729 
.0758 
.0787 
.0816 
.0846 

.0875 
.0904 
.0934 
.0963 
.0992 
.1022 

.1051 
.1080 
.1110 
.1139 
.1169 
.1198 

.1228 
.1257 
.1287 
.1317 
.1346 
.1376 

.1405 
.1435 
.1465 
.1495 
.1524 
.1554 

.1584 



.4637 
.7648 
.9409 
.0658 
.1627 

.2419 
.3089 
.3669 
.4181 
.4638 
.5053 

.5431 
.5779 
.6101 
.6401 
.6682 
.6945 

.7194 

.7429 
.7652 
.7865 
.8067 
.8261 

.8446 
.8624 
.8795 
.8960 
.9118 
.9272 

.9420 
.9563 
.9701 
.9836 
.9966 
.0093 

.0216 
.0336 
.0453 
.0567 
.0678 
.0786 

.0891 
.0995 
.1096 
.1194 
.1291 
.1385 

.1478 
.1569 
.1658 
.1745 
.1831 
.1915 

.1997 



Cotangent 
Value Logio 



343.77 
171.89 
114.59 

85.940 
68.750 

57.290 
49.104 
42.964 
38.188 
34.368 
31.242 

28.636 
26.432 
24.542 
22.904 
21.470 
20.206 

19.081 
18.075 
17.169 
16.350 
15.605 
14.924 

14.301 
13.727 
13.197 
12.706 
12.251 
11.826 

11.430 
11.059 
10.712 
10.385 
10.078 
9.7882 

9.5144 
9.2553 
9.0098 
8.7769 
8.5555 
8.3450 

8.1443 
7.9530 
7.7704 
7.5958 

7.4287 
7.2687 

7.1154 

6.9682 
6.8269 
6.6912 
6.5606 
6.4348 



.5363 
.2352 
.0591 
.9342 
.8373 

.7581 
.6911 
.6331 
.5819 
.5362 
.4947 

.4569 
.4221 
.3899 
.3599 
.3318 
.3055 

.2806 
.2571 
.2348 
.2135 
.1933 
.1739 

.1554 
.1376 
.1205 
.1040 
.0882 
.0728 

.0580 
.0437 
.0299 
.0164 
.0034 
.9907 

.9784 
.9664 
.9547 
.9433 
.9322 
.9214 

.9109 
.9005 
.8904 
.8806 
.8709 
.8615 

.8522 
.8431 
.8342 
.8255 
.8169 
.8085 



6.3138 .8003 



Cosine 
Value Logio 



1.0000 
1.0000 
1.0000 
1.0000 
.9999 
.9999 

.9998 
.9998 
.9997 
.9997 
.9996 
.9995 

.9994 
.9993 
.9992 
.9990 
.9989 
.9988 

.9986 
.9985 
.9983 
.9981 
.9980 
.9978 

.9976 
.9974 
.9971 
.9969 
.9967 
.9964 

.9962 
.9959 
.9957 
.9954 
.9951 
.9948 

.9945 
.9942 
.9939 
.9936 
.9932 
.9929 

.9925 
.9922 
.9918 
.9914 
.9911 
.9907 

.9903 
.9899 
.9894 
.9890 
.9886 
.9881 



.0000 
.0000 
.0000 
.0000 
.0000 
.0000 

.9999 
.9999 
.9999 
.9999 
.9998 
.9998 

.9997 
.9997 
.9996 
.9996 
.9995 
.9995 

.9994 
.9993 
.9993 
.9992 
.9991 
.9990 

.9989 
.9989 
.9988 
.9987 
.9986 
.9985 

.9983 
.9982 
.9981 
.9980 
.9979 
.9977 

.9976 
.9975 
.9973 
.9972 
.9971 
.9969 

.9968 
.9966 
.9964 
.9963 
.9961 
.9959 

.9958 
.9956 
.9954 
.9952 
.9950 
.9948 



.9877 .9946 



90° 00 

50 
40 
30 
20 
10 

89° 00' 

50 
40 
30 
20 
10 

88° 00 

50 
40 
30 
20 
10 

87° 00 

50 
40 
30 
20 
10 

86° 00 

50 
40 
30 
20 
10 

85° 00 

50 
40 
30 
20 
10 

84° 00 

50 
40 
30 
20 
10 

83° 00 

50 
40 
30 
20 
10 

82° 00 

50 
40 
30 
20 
10 

81° 00 



1.5708 
1.5679 
1.5650 
1.5621 
1.5592 
1.5563 

1.5533 
1.5504 
1.5475 
1.5446 
1.5417 
1.5388 

1.5359 
1.5330 
1.5301 
1.5272 
1.5243 
1.5213 

1.5184 
1.5155 
1.5126 
1.5097 
1.5068 
1.5039 

1.5010 
1.4981 
1.4952 
1.4923 
1.4893 
1.4864 

1.4835 
1.4806 
1.4777 
1.4748 
1.4719 
1.4690 

1.4661 
1.4632 
1.4603 
1.4573 
1.4544 
1.4515 

1.4486 
1.4457 
1.4428 
1.4399 
1.4370 
1.4341 

1.4312 
1.4283 
1.4254 
1.4224 
1.4195 
1.4166 

1.4137 



Value Logio 
Cosine 



Value Logio 
Cotangent 



Value Logio 
Tangent 



Value Logio 

Sine 



Degrees 



Radians 



XIV c] Four Place Trigonometric Functions 

[Characteristics of Logarithms omitted — determine by the usual rule from the value] 



139 



Radians 



,1571 
1600 
,1629 
,1658 
1687 
1716 

1745 
1774 
1804 
1833 
1862 
1891 

1920 
1949 
1978 
.2007 
.2036 
.2065 

.2094 
.2123 
.2153 
.2182 
.2211 
.2240 

.2269 
.2298 
.2327 
.2356 
.2385 
.2414 

.2443 
.2473 
.2502 
.2531 
.2560 
.2589 

.2618 
.2647 
.2676 
.2705 
.2734 
.2763 

.2793 

.2822 
.2851 
.2880 
.2909 
.2938 

.2967 
.2996 
.3025 
.3054 
.3083 
.3113 

.3142 



Degrees 



9° 00' 

10 
20 
30 
40 
50 

10° 00' 

10 
20 
30 
40 
50 

11° 00' 

10 
20 
30 
40 
50 

12° 00' 

10 
20 
30 
40 
50 

13° 00' 

10 
20 
30 
40 
50 

14° 00' 

10 
20 
30 
40 
50 

15° 00' 

10 
20 
30 
40 
50 

16° 00' 

10 
20 
30 
40 
50 

17° 00' 

10 
20 
30 
40 
50 

18° 00' 



Sine 
Value Logio 



1564 
1593 
1622 
1650 
1679 
1708 

1736 
1765 
1794 
1822 
1851 
1880 

1908 
1937 
1965 
1994 
2022 
2051 

2079 
2108 
2136 
2164 
2193 
2221 

2250 

2278 
2306 
2334 
2363 
2391 

2419 
2447 
2476 
2504 
2532 
2560 

,2588 
2616 
,2644 

,2672 
2700 

,2728 

,2756 

,2784 
.2812 
.2840 
.2868 
.2896 

.2924 
.2952 
.2979 
.3007 
.3035 
.3062 

.3090 



.1943 
.2022 
.2100 
.2176 
.2251 
.2324 

.2397 

.2468 
.2538 
.2606 
.2674 
.2740 

.2806 
.2870 
.2934 
.2997 
.3058 
.3119 

.3179 
.3238 
.3296 
.3353 
.3410 
.3466 

.3521 
.3575 
.3629 
.3682 
.3734 
.3786 

.3837 
.3887 
.3937 
.3986 
.4035 
.4083 

.4130 
.4177 
.4223 
.4269 
.4314 
.4359 

.4403 
.4447 
.4491 
.4533 
.4576 
.4618 

.4659 
.4700 
.4741 
.4781 
.4821 
.4861 

.4900 



Value Logio 
Cosine 



Tangent 
Value Logio 



.1584 
1614 
.1644 
.1673 
.1703 
.1733 

.1763 
.1793 
.1823 
.1853 

.1883 
.1914 

1944 
.1974 
.2004 
.2035 
.2065 
.2095 

.2126 
.2156 
.2186 
.2217 
.2247 
.2278 

.2309 
.2339 
.2370 
.2401 
.2432 
.2462 

.2493 
.2524 
.2555 
.2586 
.2617 
.2648 

.2679 
.2711 

.2742 
.2773 
.2805 
.2836 

.2867 
.2899 
.2931 
.2962 
.2994 
.3026 

.3057 
.3089 
.3121 
.3153 
.3185 
.3217 

.3249 



1997 
.2078 
.2158 
.2236 
.2313 
.2389 

.2463 
.2536 
.2609 
.2680 
.2750 
.2819 

.2887 
.2953 
.3020 
.3085 
.3149 
.3212 

.3275 
.3336 
.3397 
.3458 
.3517 
.3576 

.3634 
.3691 
.3748 
.3804 
.3859 
.3914 

.3968 
.4021 
.4074 
.4127 
.4178 
.4230 

.4281 
.4331 
.4381 
.4430 
.4479 
.4527 

.4575 
.4622 
.4669 
.4716 
.4762 
.4808 

.4853 
.4898 
.4943 
.4987 
.5031 
.5075 

.5118 



Value Logio 
Cotangent 



Cotangent 
Value Logio 



6.3138 
6.1970 
6.0844 
5.9758 
5.8708 
5.7694 

5.6713 
5.5764 
5.4845 
5.3955 
5.3093 
5.2257 

5.1446 
5.0658 
4.9894 
4.9152 
4.8430 
4.7729 

4.7046 
4.6382 
4.5736 
4.5107 
4.4494 
4.3897 

4.3315 

4.2747 
4.2193 
4.1653 
4.1126 
4.0611 

4.0108 
3.9617 
3.9136 
3.8667 
3.8208 
3.7760 

3.7321 
3.6891 
3.6470 
3.6059 
3.5656 
3.5261 

3.4874 
3.4495 
3.4124 
3.3759 
3.3402 
3.3052 



2709 
2371 
2041 
1716 
1397 
1084 



.8003 
.7922 
.7842 
.7764 
.7687 
.7611 

.7537 

.7464 
.7391 
.7320 
.7250 
.7181 

.7113 

.7047 
.6980 
.6915 
.6851 

.6788 

.6725 
.6664 
.6603 
.6542 
.6483 
.6424 

.6366 
.6309 
.6252 
.6196 
.6141 
.6086 

.6032 
.5979 
.5926 
.5873 

.5822 
.5770 

.5719 
.5669 
.5619 
.5570 
.5521 
.5473 

.5425 
.5378 
.5331 
.5284 
.5238 
.5192 

.5147 
.5102 
.5057 
.5013 
.4969 
.4925 



3.0777 .4882 



Value Logio 
Tangent 



Cosine 
Value Logio 



.9877 
.9872 
.9868 
.9863 
.9858 
.9853 

.9848 
.9843 
.9838 
.9833 

.9827 
.9822 

.9816 
.9811 
.9805 
.9799 
.9793 
.9787 

.9781 
.9775 
.9769 
.9763 
.9757 
.9750 

.9744 
.9737 
.9730 
.9724 
.9717 
.9710 

.9703 
.9696 
.9689 
.9681 
.9674 
.9667 

.9659 
.9652 
.9644 
.9636 
.9628 
.9621 

.9613 
.9605 
.9596 
.9588 
.9580 
.9572 

.9563 
.9555 
.9546 
.9537 
.9528 
.9520 

.9511 . : 



.9946 
.9944 
.9942 
.9940 
.9938 
.9936 

.9934 
.9931 
.9929 
.9927 
.9924 
.9922 

.9919 
.9917 
.9914 
.9912 
.9909 
.9907 

.9904 
.9901 
.9899 
.9896 
.9893 
.9890 

.9887 
.9884 
.9881 
.9878 
.9875 
.9872 

.9869 
.9866 
.9863 
.9859 
.9856 
.9853 

.9849 
.9846 
.9843 
.9839 
.9836 
.9832 

.9828 
.9825 
.9821 
.9817 
.9814 
.9810 

.9806 
.9802 
.9798 
.9794 
.9790 
.9786 



Value Logio 
Sine 



81° 00' 

50 
40 
30 
20 
10 

80° 00' 

50 
40 
30 
20 
10 

79° 00' 

50 
40 
30 
20 
10 

78° 00' 

50 
40 
30 
20 
10 

77° 00' 

50 
40 
30 
20 
10 

76° 00' 

50 
40 
30 
20 
10 

75° 00' 

50 
40 
30 
20 
10 

74° 00' 

50 
40 
30 
20 
10 

73° 00' 

50 
40 
30 
20 
10 

72° 00' 



1.4137 
1.4108 
1.4079 
1.4050 
1.4021 
1.3992 

1.3963 
1.3934 
1.3904 
1.3875 
1.3846 
1.3817 

1.3788 
1.3759 
1.3730 
1.3701 
1.3672 
1.3643 

1.3614 
1.3584 
1.3555 
1.3526 
1.3497 
1.3468 

1.3439 
1.3410 
1.3381 
1.3352 
1.3323 
1.3294 

1.3265 
1.3235 
1.3206 
1.3177 
1.3148 
1.3119 

1.3090 
1.3061 
1.3032 
1.3003 
1.2974 
1.2945 

1.2915 
1.2886 
1.2857 
1.2828 
1.2799 
1.2770 

1.2741 
1.2712 
1.2683 
1.2654 
1.2625 
1.2595 

1.2566 



Radians 



14U Four Place Trigonometric Functions [XIV c 

[Characteristics of Logarithms omitted — determine by the usual rule from the value] 



Radians 



.3142 
.3171 
.3200 
.3229 
.3258 
.3287 

.3316 
.3345 
.3374 
.3403 
.3432 
.3462 

.3491 
.3520 
.3549 
.3578 
.3607 
.3636 

.3665 
.3694 
.3723 
.3752 
.3782 
.3811 

.3840 
.3869 
.3898 
.3927 
.3956 
.3985 

.4014 
.4043 
.4072 
.4102 
.4131 
.4160 

.4189 
.4218 
.4247 
.4276 
.4305 
.4334 

.4363 
.4392 
.4422 
.4451 
.4480 
.4509 

.4538 
.4567 
.4596 
.4625 
.4654 
.4683 

.4712 



Degrees 



18° 00' 

10 
20 
30 
40 
50 

19° 00' 

10 
20 
30 
40 
50 

20° 00' 

10 
20 
30 
40 
50 

21° 00' 

10 
20 
30 
40 
50 

22° 00' 

10 
20 
30 
40 
50 

23° 00' 

10 
20 
30 
40 
50 

24° 00' 

10 
20 
30 
40 
50 

25° 00' 

10 
20 
30 
40 
50 

26° 00' 

10 
20 
30 
40 
50 

27° 00' 



Sine 
Value Logio 



3090 
3118 
3145 
3173 
3201 
3228 

3256 
3283 
3311 
3338 
3365 
3393 

3420 
3448 
3475 
3502 
3529 
3557 

3584 
3611 
3638 
3665 
3692 
3719 

3746 
3773 
3800 
3827 
3854 
3881 

3907 
3934 
3961 
3987 
4014 
4041 

4067 
4094 
4120 
4147 
4173 
4200 

,4226 
,4253 
,4279 
,4305 
,4331 
.4358 

.4384 
.4410 
.4436 
.4462 
.4488 
.4514 

.4540 .6570 



.4900 
.4939 
.4977 
.5015 
.5052 
.5090 

.5126 
.5163 
.5199 
.5235 
.5270 
.5306 

.5341 
.5375 
.5409 
.5443 
.5477 
.5510 

.5543 
.5576 
.5609 
.5641 
.5673 
.5704 

.5736 
.5767 
.5798 

.5828 
.5859 
.5889 

.5919 

.5948 
.5978 
.6007 
.6036 
.6065 

.6093 
.6121 
.6149 
.6177 
.6205 
.6232 

.6259 
.6286 
.6313 
.6340 
.6366 
.6392 

.6418 
.6444 
.6470 
.6495 
.6521 
.6546 



Value Logio 
Cosine 



Tangent 
Value Logio 



.3249 
.3281 
.3314 
.3346 
.3378 
.3411 

.3443 
.3476 
.3508 
.3541 
.3574 
.3607 

.3640 
.3673 
.3706 
.3739 
.3772 
.3805 

.3839 

.3872 
.3906 
.3939 
.3973 
.4006 

.4040 
.4074 
.4108 
.4142 
.4176 
.4210 

.4245 
.4279 
.4314 
.4348 
.4383 
.4417 

.4452 
.4487 
.4522 
.4557 
.4592 
.4628 

.4663 
.4699 
.4734 
.4770 
.4806 
.4841 

.4877 
.4913 
.4950 
.4986 
.5022 
.5059 

.5095 



.5118 
.5161 
.5203 
.5245 

.5287 
.5329 

.5370 
.5411 
.5451 
.5491 
.5531 
.5571 

.5611 
.5650 
.5689 
.5727 
.5766 
.5804 

.5842 
.5879 
.5917 
.5954 
.5991 
.6028 

.6064 
.6100 
.6136 
.6172 
.6208 
.6243 

.6279 
.6314 
.6348 
.6383 
.6417 
.6452 

.6486 
.6520 
.6553 
.6587 
.6620 
.6654 

.6687 
.6720 
.6752 
.6785 
.6817 
.6850 

.6882 
.6914 
.6946 
.6977 
.7009 
.7040 

.7072 



Value Logio 
Cotangent 



Cotangent 
Value Logio 



3.0777 
3.0475 
3.0178 
2.9887 
2.9600 
2.9319 

2.9042 
2.8770 
2.8502 
2.8239 
2.7980 
2.7725 

2.7475 

2.7228 
2.6985 
2.6746 
2.6511 
2.6279 

2.6051 
2.5826 
2.5605 
2.5386 
2.5172 
2.4960 

2.4751 
2.4545 
2.4342 
2.4142 
2.3945 
2.3750 

2.3559 
2.3369 
2.3183 
2.2998 
2.2817 
2.2637 

2.2460 
2.2286 
2.2113 
2.1943 
2.1775 
2.1609 

2.1445 
2.1283 
2.1123 
2.0965 
2.0809 
2.0655 

2.0503 
2.0353 
2.0204 
2.0057 
1.9912 
1.9768 

1.9626 



.4882 
.4839 
.4797 
.4755 
.4713 
.4671 

.4630 
.4589 
.4549 
.4509 
.4469 
.4429 

.4389 
.4350 
.4311 
.4273 
.4234 
.4196 

.4158 
.4121 
.4083 
.4046 
.4009 
.3972 

.3936 
.3900 
.3864 
.3828 
.3792 
.3757 

.3721 
.3686 
.3652 
.3617 
.3583 
.3548 

.3514 
.3480 
.3447 
.3413 
.3380 
.3346 

.3313 

.3280 
.3248 
.3215 
.3183 
.3150 

.3118 

.3086 
.3054 
.3023 
.2991 
.2960 

.2928 



Value Logio 
Tangent 



Cosine 
Value Logio 



.9511 
.9502 
.9492 
.9483 
.9474 
.9465 

.9455 
.9446 
.9436 
.9426 
.9417 
.9407 

.9397 
.9387 
.9377 
.9367 
.9356 
.9346 

.9336 
.9325 
.9315 
.9304 
.9293 
.9283 

.9272 
.9261 
.9250 
.9239 
.9228 
.9216 

.9205 
.9194 
.9182 
.9171 
.9159 
.9147 

.9135 
.9124 
.9112 
.9100 

.9088 
.9075 

.9063 
.9051 
.9038 
.9026 
.9013 
.9001 

.8988 
.8975 
.8962 
.8949 
.8936 
.8923 

.8910 



.9782 
.9778 
.9774 
.9770 
.9765 
.9761 

.9757 
.9752 
.9748 
.9743 
.9739 
.9734 

.9730 
.9725 
.9721 
.9716 
.9711 
.9706 

.9702 
.9697 
.9692 
.9687 
.9682 
.9677 

.9672 
.9667 
.9661 
.9656 
.9651 
.9646 

.9640 
.9635 
.9629 
.9624 
.9618 
.9613 

.9607 
.9602 
.9596 
.9590 
.9584 
.9579 

.9573 
.9567 
.9561 
.9555 
.9549 
.9543 

.9537 
.9530 
.9524 
.9518 
.9512 
.9505 

.9499 



Value Logio 
Sine 



72° 00' 

50 
40 
30 
20 
10 

71° 00' 

50 
40 
30 
20 
10 

70° 00' 

50 
40 
30 
20 
10 

69° 00' 

50 
40 
30 
20 
10 

68° 00' 

50 
40 
30 
20 
10 

67° 00' 

50 
40 
30 
20 
10 

66° 00' 

50 
40 
30 
20 
10 

65° 00' 

50 
40 
30 
20 
10 

64° 00' 

50 
40 
30 
20 
10 

63° 00' 



Degrees 



1.2566 
1.2537 
1.2508 
1.2479 
1.2450 
1.2421 

1.2392 
1.2363 
1.2334 
1.2305 
1.2275 
1.2246 

1.2217 
1.2188 
1.2159 
1.2130 
1.2101 
1.2072 

1.2043 
1.2014 
1.1985 
1.1956 
1.1926 
1.1897 

1.1868 
1.1839 
1.1810 
1.1781 
1.1752 
1.1723 

1.1694 
1.1665 
1.1636 
1.1606 
1.1577 
1.1548 

1.1519 
1.1490 
1.1461 
1.1432 
1.1403 
1.1374 

1.1345 
1.1316 
1.1286 
1.1257 
1.1228 
1.1199 

1.1170 
1.1141 
1.1112 
1.1083 
1.1054 
1.1025 

1.0996 



Radians 



XIV c] Four Place Trigonometric Functions 141 

[Characteristics of Logarithms omitted — determine by the usual rule from the value] 



Radians 



.4712 
.4741 
.4771 
.4800 

.4829 
.4858 

.4887 
.4916 
.4945 
.4974 
.5003 
.5032 

.5061 
.5091 
.5120 
.5149 
.5178 
.5207 

.5236 
.5265 
.5294 
.5323 
.5352 
.5381 

.5411 
.5440 
.5469 
.5498 
.5527 
.5556 

.5585 
.5614 
.5643 
.5672 
.5701 
.5730 

.5760 
.5789 
.5818 
.5847 
.5876 
.5905 

.5934 
.5963 
.5992 
.6021 
.6050 
.6080 

.6109 
.6138 
.6167 
.6196 
.6225 
.6254 

.6283 



Degrees 



27° 00' 

10 
20 
30 
40 
50 

28° 00' 

10 
20 
30 
40 
50 

29° 00' 

10 
20 
30 
40 
50 

30° 00' 

10 
20 
30 
40 
50 

31° 00' 

10 
20 
30 
40 
50 

32° 00' 

10 
20 
30 
40 
50 

33° 00' 

10 
20 
30 
40 
50 

34° 00' 

10 
20 
30 
40 
50 

35° 00' 

10 
20 
30 
40 
50 

36° 00' 



Sine 
Value Logio 



.4540 
.4566 
.4592 
.4617 
.4643 
.4669 

.4695 
.4720 
.4746 

.4772 
.4797 
.4823 

.4848 
.4874 
.4899 
.4924 
.4950 
.4975 

.5000 
.5025 
.5050 
.5075 
.5100 
.5125 

.5150 
.5175 
.5200 
.5225 
.5250 
.5275 

.5299 
.5324 
.5348 
.5373 
.5398 
.5422 

.5446 
.5471 
.5495 
.5519 
.5544 
.5568 

.5592 
.5616 
.5640 
.5664 
.5688 
.5712 

.5736 
.5760 
.5783 
.5807 
.5831 
.5854 

.5878 



.6570 
.6595 
.6620 
.6644 
.6668 
.6692 

.6716 
.6740 
.6763 
.6787 
.6810 
.6833 

.6856 
.6878 
.6901 
.6923 
.6946 
.6968 

.6990 
.7012 
.7033 
.7055 
.7076 
.7097 

.7118 
.7139 
.7160 
.7181 
.7201 
.7222 

.7242 
.7262 
.7282 
.7302 
.7322 
.7342 

.7361 
.7380 
.7400 
.7419 
.7438 
.7457 

.7476 
.7494 
.7513 
.7531 
.7550 
.7568 

.7586 
.7604 
.7622 
.7640 
.7657 
.7675 

.7692 



Value Logio 
Cosine 



Tangent 
Value Logio 



.5095 
.5132 
.5169 
.5206 
.5243 
.5280 

.5317 
.5354 
.5392 
.5430 
.5467 
.5505 

.5543 
.5581 
.5619 
.5658 
.5696 
.5735 

.5774 
.5812 
.5851 
.5890 
.5930 
.5969 

.6009 
.6048 
.6088 
.6128 
.6168 
.6208 

.6249 
.6289 
.6330 
.6371 
.6412 
.6453 

.6494 
.6536 
.6577 
.6619 
.6661 
.6703 

.6745 
.6787 
.6830 
.6873 
.6916 
.6959 

.7002 
.7046 
.7089 
.7133 
.7177 
.7221 

.7265 



.7072 
.7103 
.7134 
.7165 
.7196 
.7226 

.7257 

.7287 
.7317 
.7348 
.7378 
.7408 

.7438 
.7467 
.7497 
.7526 
.7556 
.7585 

.7614 
.7644 
.7673 
.7701 
.7730 
.7759 

.7788 
.7816 
.7845 
.7873 
.7902 
.7930 

.7958 
.7986 
.8014 
.8042 
.8070 
.8097 

.8125 
.8153 
.8180 
.8208 
.8235 
.8263 

.8290 
.8317 
.8344 
.8371 
.8398 
.8425 

.8452 
.8479 
.8506 
.8533 
.8559 
.8586 

.8613 



Value Logio 
Cotangent 



Cotangent 
Value Logio 



1.9626 
1.9486 
1.9347 
1.9210 
1.9074 
1.8940 

1.8807 
1.8676 
1.8546 
1.8418 
1.8291 
1.8165 

1.8040 
1.7917 
1.7796 
1.7675 
1.7556 
1.7437 

1.7321 
1.7205 
1.7090 
1.6977 
1.6864 
1.6753 

1.6643 
1.6534 
1.6426 
1.6319 
1.6212 
1.6107 

1.6003 
1.5900 
1.5798 
1.5697 
1.5597 
1.5497 

1.5399 
1.5301 
1.5204 
1.5108 
1.5013 
1.4919 

1.4826 
1.4733 
1.4641 
1.4550 
1.4460 
1.4370 

1.4281 
1.4193 
1.4106 
1.4019 
1.3934 
1.3848 

1.3764 .1387 



.2928 

.2897 
.2866 
.2835 
.2804 

.2774 

.2743 
.2713 
.2683 
.2652 
.2622 
.2592 

.2562 
.2533 
.2503 
.2474 
.2444 
.2415 

.2386 
.2356 
.2327 
.2299 
.2270 
.2241 

.2212 
.2184 
.2155 
.2127 

.2098 
.2070 

.2042 
.2014 
.1986 
.1958 
.1930 
.1903 

.1875 
.1847 
.1820 
.1792 
.1765 
.1737 

.1710 
.1683 
.1656 
.1629 
.1602 
.1575 

.1548 
.1521 
.1494 
.1467 
.1441 
.1414 



Cosine 
Value Logio 



Value Logio 
Tangent 



.8910 
.8897 

.8884 
.8870 
.8857 
.8843 

.8829 
.8816 
.8802 
.8788 
.8774 
.8760 

.8746 

.8732 
.8718 
.8704 
.8689 
.8675 

.8660 
.8646 
.8631 
.8616 
.8601 
.8587 

.8572 
.8557 
.8542 
.8526 
.8511 
.8496 

.8480 
.8465 
.8450 
.8434 
.8418 
.8403 

.8387 
.8371 
.8355 
.8339 
.8323 
.8307 

.8290 

.8274 
.8258 
.8241 
.8225 
.8208 

.8192 
.8175 
.8158 
.8141 
.8124 
.8107 



.9499 
.9492 
.9486 
.9479 
.9473 
.9466 

.9459 
.9453 
.9446 
.9439 
.9432 
.9425 

.9418 
.9411 
.9404 
.9397 
.9390 
.9383 

.9375 
.9368 
.9361 
.9353 
.9346 
.9338 

.9331 
.9323 
.9315 
.9308 
.9300 
.9292 

.9284 
.9276 
.9268 
.9260 
.9252 
.9244 

.9236 
.9228 
.9219 
.9211 
.9203 
.9194 

.9186 
.9177 
.9169 
.9160 
.9151 
.9142 

.9134 
.9125 
.9116 
.9107 
.9098 
.9089 



,8090 .9080 



Value Logio 
Sine 



63° 00' 

50 
40 
30 
20 
10 

62° 00' 

50 
40 
30 
20 
10 

61° 00' 

50 
40 
30 
20 
10 

60° 00' 

50 
40 
30 
20 
10 

59° 00' 

50 
40 
30 
20 
10 

58° 00' 

50 
40 
30 
20 
10 

57° 00' 

50 
40 
30 
20 
10 

56° 00' 

50 
40 
30 
20 
10 

55° 00' 

50 
40 
30 
20 
10 

54° 00' 



Degrees 



1.0996 
1.0966 
1.0937 
1.0908 
1.0879 
1.0850 

1.0821 
1.0792 
1.0763 
1.0734 
1.0705 
1.0676 

1.0647 
1.0617 
1.0588 
1.0559 
1.0530 
1.0501 

1.0472 
1.0443 
1.0414 
1.0385 
1.0356 
1.0327 

1.0297 
1.0268 
1.0239 
1.0210 
1.0181 
1.0152 

1.0123 
1.0094 
1.0065 
1.0036 
1.0007 
.9977 

.9948 
.9919 
.9890 
.9861 
.9832 
.9803 

.9774 
.9745 
.9716 
.9687 
.9657 
.9628 

.9599 
.9570 
.9541 
.9512 
.9483 
.9454 

.9425 



Radians 



142 Four Place Trigonometric Functions [XIV c 

[Characteristics of Logarithms omitted — determine by the usual rule from the value] 



Radians 



.6283 
.6312 
.6341 
.6370 
.6400 
.6429 

.6458 
.6487 
.6516 
.6545 
.6574 
.6603 

.6632 
.6661 
.6690 
.6720 
.6749 
.6778 

.6807 
.6836 
.6865 
.6894 
.6923 
.6952 

.6981 
.7010 
.7039 
.7069 
.7098 
.7127 

.7156 
.7185 
.7214 
.7243 

.7272 
.7301 

.7330 
.7359 
.7389 
.7418 

.7447 
.7476 

.7505 
.7534 
.7563 
.7592 
.7621 
.7650 

.7679 
.7709 

.7738 
.7767 
.7796 
.7825 

.7854 



Degrees 



36° 00 

10 
20 
30 
40 
50 

37° 0O 

10 
20 
30 
40 
50 

38° 00' 

10 
20 
30 
40 
50 

39° 00 

10 
20 
30 
40 
50 

40° 00 

10 
20 
30 
40 
50 

41° 00 

10 
20 
30 
40 
50 

42° 00' 

10 
20 
30 
40 
50 

43° 00 

10 

20 
30 
40 
50 

44° 00 

10 
20 
30 
40 
50 

45° 00 



Sine 
Value Logio 



,5878 
5901 
5925 
5948 
5972 
5995 

6018 
6041 
6065 
6088 
6111 
6134 

6157 
6180 
6202 
6225 
6248 
6271 

6293 
6316 
6338 
6361 
6383 
6406 

6428 
6450 
6472 
6494 
6517 
6539 

6561 
6583 
6604 
6626 
6648 
6670 

6691 
6713 
6734 
6756 
6777 
6799 

,6820 
6841 
6862 
6884 
6905 
6926 

6947 
6967 
,6988 
7009 
,7030 
,7050 

.7071 



.7692 
.7710 
.7727 
.7744 
.7761 
.7778 

.7795 
.7811 

.7828 
.7844 
.7861 

.7877 

.7893 
.7910 
.7926 
.7941 
.7957 
.7973 

.7989 
.8004 
.8020 
.8035 
.8050 
.8066 

.8081 
.8096 
.8111 
.8125 
.8140 
.8155 

.8169 

.8184 
.8198 
.8213 
.8227 
.8241 

.8255 

.8269 
.8283 
.8297 
.8311 
.8324 

.8338 
.8351 
.8365 
.8378 
.8391 
.8405 

.8418 
.8431 
.8444 
.8457 
.8469 
.8482 

.8495 



Value Logio 
Cosine 



Tangent 
Value Logio 



.7265 
.7310 
.7355 
.7400 
.7445 
.7490 

.7536 
.7581 
.7627 
.7673 
.7720 
.7766 

.7813 

.7860 
.7907 
.7954 
.8002 
.8050 

.8098 
.8140 
.8195 
.8243 
.8292 
.8342 

.8391 
.8441 
.8491 
.8541 
.8591 
.8642 

.8693 

.8744 
.8796 
.8847 
.8899 
.8952 

.9004 
.9057 
.9110 
.9163 
.9217 
.9271 

.9325 
.9380 
.9435 
.9490 
.9545 
.9601 

.9657 
.9713 
.9770 
.9827 

.9884 
.9942 

1.0000 .0000 



.8613 
.8639 
.8666 
.8692 

.8718 
.8745 

.8771 
.8797 
.8824 
.8850 
.8876 
.8902 

.8928 
.8954 
.8980 
.9006 
.9032 
.9058 

.9084 
.9110 
.9135 
.9161 
.9187 
.9212 

.9238 
.9264 
.9289 
.9315 
.9341 
.9366 

.9392 
.9417 
.9443 
.9468 
.9494 
.9519 

.9544 
.9570 
.9595 
.9621 
.9646 
.9671 

.9697 
.9722 
.9747 
.9772 
.9798 
.9823 

.9848 
.9874 
.9899 
.9924 
.9949 
.9975 



Value Logio 
Cotangent 



Cotangent 
Value Logio 



1.3764 
1.3680 
1.3597 
1.3514 
1.3432 
1.3351 

1.3270 
1.3190 
1.3111 
1.3032 
1.2954 
1.2876 



1.2799 
1.2723 
1.2647 
1.2572 
1.2497 
1.2423 

1.2349 
1.2276 
1.2203 
1.2131 
1.2059 
1.1988 

1.1918 
1.1847 
1.1778 
1.1708 
1.1640 
1.1571 

1.1504 
1.1436 
1.1369 
1.1303 
1.1237 
1.1171 

1.1106 
1.1041 
1.0977 
1.0913 
1.0850 
1.0786 

1.0724 
1.0661 
1.0599 
1.0538 
1.0477 
1.0416 

1.0355 
1.0295 
1.0235 
1.0176 
1.0117 
1.0058 



.1387 
.1361 
.1334 
.1308 
.1282 
.1255 

.1229 
.1203 
.1176 
.1150 
.1124 
.1098 

.1072 
.1046 
.1020 
.0994 
.0968 
.0942 

.0916 
.0890 
.0865 
.0839 
.0813 
.0788 

.0762 
.0736 
.0711 
.0685 
.0659 
.0634 

.0608 
.0583 
.0557 
.0532 
.0506 
.0481 

.0456 
.0430 
.0405 
.0379 
.0354 
.0329 

.0303 
.0278 
.0253 
.0228 
.0202 
.0177 

.0152 
.0126 
.0101 
.0076 
.0051 
.0025 



1.0000 .0000 



Value Logio 
Tangent 



Cosine 
Value Logio 



.8090 
.8073 
.8056 
.8039 
.8021 
.8004 

.7986 
.7969 
.7951 
.7934 
.7916 
.7898 

.7880 
.7862 
.7844 
.7826 
-7808 
.7790 

.7771 
.7753 
.7735 
.7716 
.7698 
.7679 

.7660 
.7642 
.7623 

.7604 
.7585 
.7566 

.7547 
.7528 
.7509 
.7490 
.7470 
.7451 

.7431 
.7412 
.7392 
.7373 
.7353 
.7333 

.7314 
.7294 
.7274 
.7254 
.7234 
.7214 

.7193 
.7173 
.7153 
.7133 
.7112 
.7092 

.7071 



.9080 
.9070 
.9061 
.9052 
.9042 
.9033 

,9023 
.9014 
.9004 
.8995 
.8985 
.8975 

.8965 
.8955 
.8945 
.8935 
.8925 
.8915 

.8905 

.8895 
.8884 
.8874 
.8864 
.8853 

.8843 
.8832 
.8821 
.8810 
.8800 
.8789 

.8778 
.8767 
.8756 
.8745 
.8733 
.8722 

.8711 
.8699 
.8688 
.8676 
.8665 
.8653 

.8641 
.8629 
.8618 
.8606 
.8594 
.8582 

.8569 
.8557 
.8545 
.8532 
.8520 
.8507 

.8495 



Value Logio 
Sine 



54° 00' 

50 
40 
30 
20 
10 

53° 00' 

50 
40 
30 
20 
10 

52° 00' 

50 
40 
30 
20 
10 

51° 00 

50 
40 
30 
20 
10 

50° 00 

50 
40 
30 
20 
10 

49° 00 

50 
40 
30 
20 
10 

48° 00 

50 
40 
30 
20 
10 

47°00 / 

50 
40 
30 
20 
10 

46° 00 

50 
40 
30 
20 
10 

45° 00' 



Degrees 



.9425 
.9396 
.9367 
.9338 
.9308 
.9279 

.9250 
.9221 
.9192 
.9163 
.9134 
.9105 

.9076 
.9047 
.9018 
.8988 
.8959 
.8930 

.8901 

.8872 
.8843 
.8814 
.8785 
.8756 

.8727 
.8698 
.8668 
.8639 
.8610 
.8581 

.8552 
.8523 
.8494 
.8465 
.8436 
.8407 

.8378 
.8348 
.8319 
.8290 
.8261 
.8232 

.8203 
.8174 
.8145 
.8116 
.8087 
.8058 

.8029 
.7999 
.7970 
.7941 
.7912 
.7883 

.7854 



Radians 



SLIDE-RULE 



~w 






li 

(1) (2) (3) 



n 



in 



li, 

i 






r-r-n 



n 



WM 



(4) 



li 



1 ' 



B' 



lJ_L, 
(5) 



Directions 



A reasonably accurate slide-rule 
may be made by the student, for 
temporary practice, as follows. 
Take three strips of heavy stiff 
cardboard 1".3 wide by 6" long; 
these are shown in cross-section in 
(1), (2), (3) above. On (3) 
paste or glue the adjoining cut 
of the slide rule. Then cut strips 
(2) and (3) accurately along the 
lines marked. Paste or glue the 
pieces together as shown in (4) 
and (5). Then (5) forms the 
slide of the slide-rule, and it will 
fit in the groove in (4) if the work 
has been carefully done. Trim 
off the ends as shown in the large 
cut. 







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